메뉴 건너뛰기




Volumn 47, Issue 2, 2010, Pages 871-890

A new two-step hybrid method for the numerical solution of the Schrödinger equation

Author keywords

Explicit methods; Hybrid methods; Multistep methods; Phase fitted; Phase lag; Schr dinger equation

Indexed keywords


EID: 77952955163     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10910-009-9606-5     Document Type: Article
Times cited : (108)

References (150)
  • 6
    • 0141730856 scopus 로고    scopus 로고
    • Numerical methods for 1D, 2D and 3D differential equations arising in chemical problems
    • Simos T. E.: Numerical methods for 1D, 2D and 3D differential equations arising in chemical problems. Chem. Modell. Appl. Theory 2, 170-270 (2002).
    • (2002) Chem. Modell. Appl. Theory , vol.2 , pp. 170-270
    • Simos, T.E.1
  • 7
    • 0001237676 scopus 로고    scopus 로고
    • On finite difference methods for the solution of the Schrödinger equation
    • Simos T. E., Williams P. S.: On finite difference methods for the solution of the Schrödinger equation. Comput. Chem. 23, 513-554 (1999).
    • (1999) Comput. Chem. , vol.23 , pp. 513-554
    • Simos, T.E.1    Williams, P.S.2
  • 9
    • 0000913326 scopus 로고    scopus 로고
    • On the construction of exponentially-fitted methods for the numerical solution of the Schrödinger equation
    • Konguetsof A., Simos T. E.: On the construction of exponentially-fitted methods for the numerical solution of the Schrödinger equation. J. Comput. Method Sci. Eng. 1, 143-165 (2001).
    • (2001) J. Comput. Method Sci. Eng. , vol.1 , pp. 143-165
    • Konguetsof, A.1    Simos, T.E.2
  • 10
    • 0002481902 scopus 로고
    • Exponential-fitting methods for the numerical solution of the Schrödinger equation
    • Raptis A. D., Allison A. C.: Exponential-fitting methods for the numerical solution of the Schrödinger equation. Comput. Phys. Commun. 14, 1-5 (1978).
    • (1978) Comput. Phys. Commun. , vol.14 , pp. 1-5
    • Raptis, A.D.1    Allison, A.C.2
  • 11
    • 0001176928 scopus 로고
    • Exponential multistep methods for ordinary differential equations
    • Raptis A. D.: Exponential multistep methods for ordinary differential equations. Bull. Greek Math. Soc. 25, 113-126 (1984).
    • (1984) Bull. Greek Math. Soc. , vol.25 , pp. 113-126
    • Raptis, A.D.1
  • 13
    • 0002792006 scopus 로고
    • A numerov-like scheme for the numerical solution of the Schrödinger equation in the deep continuum spectrum of energies
    • Ixaru L. G., Rizea M.: A numerov-like scheme for the numerical solution of the Schrödinger equation in the deep continuum spectrum of energies. Comput. Phys. Commun. 19, 23-27 (1980).
    • (1980) Comput. Phys. Commun. , vol.19 , pp. 23-27
    • Ixaru, L.G.1    Rizea, M.2
  • 14
    • 0036341591 scopus 로고    scopus 로고
    • A new Runge-Kutta-Nystrom method with phase-lag of order infinity for the numerical solution of the Schrödinger equation
    • Simos T. E., Williams P. S.: A new Runge-Kutta-Nystrom method with phase-lag of order infinity for the numerical solution of the Schrödinger equation. MATCH Commun. Math. Comput. Chem. 45, 123-137 (2002).
    • (2002) MATCH Commun. Math. Comput. Chem. , vol.45 , pp. 123-137
    • Simos, T.E.1    Williams, P.S.2
  • 15
    • 11044228176 scopus 로고    scopus 로고
    • Multiderivative methods for the numerical solution of the Schrödinger equation
    • Simos T. E.: Multiderivative methods for the numerical solution of the Schrödinger equation. MATCH Commun. Math. Comput. Chem. 45, 7-26 (2004).
    • (2004) MATCH Commun. Math. Comput. Chem. , vol.45 , pp. 7-26
    • Simos, T.E.1
  • 16
    • 0000172670 scopus 로고
    • Exponentially-fitted solutions of the eigenvalue Shrödinger equation with automatic error control
    • Raptis A. D.: Exponentially-fitted solutions of the eigenvalue Shrödinger equation with automatic error control. Comput. Phys. Commun. 28, 427-431 (1983).
    • (1983) Comput. Phys. Commun. , vol.28 , pp. 427-431
    • Raptis, A.D.1
  • 17
    • 0002481899 scopus 로고
    • On the numerical solution of the Schrodinger equation
    • Raptis A. D.: On the numerical solution of the Schrodinger equation. Comput. Phys. Commun. 24, 1-4 (1981).
    • (1981) Comput. Phys. Commun. , vol.24 , pp. 1-4
    • Raptis, A.D.1
  • 18
    • 0002209148 scopus 로고    scopus 로고
    • A P-stable exponentially-fitted method for the numerical integration of the Schrödinger equation
    • Zacharoula K., Simos T. E.: A P-stable exponentially-fitted method for the numerical integration of the Schrödinger equation. Appl. Math. Comput. 112, 99-112 (2000).
    • (2000) Appl. Math. Comput. , vol.112 , pp. 99-112
    • Zacharoula, K.1    Simos, T.E.2
  • 20
    • 30244503462 scopus 로고
    • Comparison of some four-step methods for the numerical solution of the Schrödinger equation
    • Ixaru L. G., Rizea M.: Comparison of some four-step methods for the numerical solution of the Schrödinger equation. Comput. Phys. Commun. 38(3), 329-337 (1985).
    • (1985) Comput. Phys. Commun. , vol.38 , Issue.3 , pp. 329-337
    • Ixaru, L.G.1    Rizea, M.2
  • 21
    • 33846421675 scopus 로고    scopus 로고
    • A family of exponentially-fitted Runge-Kutta methods with exponential order up to three for the numerical solution of the Schrödinger equation
    • Anastassi Z. A., Simos T. E.: A family of exponentially-fitted Runge-Kutta methods with exponential order up to three for the numerical solution of the Schrödinger equation. J. Math. Chem. 41(1), 79-100 (2007).
    • (2007) J. Math. Chem. , vol.41 , Issue.1 , pp. 79-100
    • Anastassi, Z.A.1    Simos, T.E.2
  • 22
    • 33750286640 scopus 로고    scopus 로고
    • Trigonometrically fitted and exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation
    • Monovasilis T., Kalogiratou Z., Simos T. E.: Trigonometrically fitted and exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation. J. Math. Chem. 40(3), 257-267 (2006).
    • (2006) J. Math. Chem. , vol.40 , Issue.3 , pp. 257-267
    • Monovasilis, T.1    Kalogiratou, Z.2    Simos, T.E.3
  • 23
    • 33750356621 scopus 로고    scopus 로고
    • The numerical solution of the radial Schrödinger equation via a trigonometrically fitted family of seventh algebraic order Predictor-Corrector methods
    • Psihoyios G., Simos T. E.: The numerical solution of the radial Schrödinger equation via a trigonometrically fitted family of seventh algebraic order Predictor-Corrector methods. J. Math. Chem. 40(3), 269-293 (2006).
    • (2006) J. Math. Chem. , vol.40 , Issue.3 , pp. 269-293
    • Psihoyios, G.1    Simos, T.E.2
  • 24
    • 33750373771 scopus 로고    scopus 로고
    • A four-step exponentially fitted method for the numerical solution of the Schrödinger equation
    • Simos T. E.: A four-step exponentially fitted method for the numerical solution of the Schrödinger equation. J. Math. Chem. 40(3), 305-318 (2006).
    • (2006) J. Math. Chem. , vol.40 , Issue.3 , pp. 305-318
    • Simos, T.E.1
  • 25
    • 17744387720 scopus 로고    scopus 로고
    • Exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation
    • Monovasilis T., Kalogiratou Z., Simos T. E.: Exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation. J. Math. Chem. 37(3), 263-270 (2005).
    • (2005) J. Math. Chem. , vol.37 , Issue.3 , pp. 263-270
    • Monovasilis, T.1    Kalogiratou, Z.2    Simos, T.E.3
  • 26
    • 17744377181 scopus 로고    scopus 로고
    • Numerical solution of the two-dimensional time independent Schrödinger equation with Numerov-type methods
    • Kalogiratou Z., Monovasilis T., Simos T. E.: Numerical solution of the two-dimensional time independent Schrödinger equation with Numerov-type methods. J. Math. Chem. 37(3), 271-279 (2005).
    • (2005) J. Math. Chem. , vol.37 , Issue.3 , pp. 271-279
    • Kalogiratou, Z.1    Monovasilis, T.2    Simos, T.E.3
  • 27
    • 17744361851 scopus 로고    scopus 로고
    • Trigonometrically fitted Runge-Kutta methods for the numerical solution of the Schrödinger equation
    • Anastassi Z. A., Simos T. E.: Trigonometrically fitted Runge-Kutta methods for the numerical solution of the Schrödinger equation. J. Math. Chem. 37(3), 281-293 (2005).
    • (2005) J. Math. Chem. , vol.37 , Issue.3 , pp. 281-293
    • Anastassi, Z.A.1    Simos, T.E.2
  • 28
    • 17744398419 scopus 로고    scopus 로고
    • Sixth algebraic order trigonometrically fitted predictor-corrector methods for the numerical solution of the radial Schrödinger equation
    • Psihoyios G., Simos T. E.: Sixth algebraic order trigonometrically fitted predictor-corrector methods for the numerical solution of the radial Schrödinger equation. J. Math. Chem. 37(3), 295-316 (2005).
    • (2005) J. Math. Chem. , vol.37 , Issue.3 , pp. 295-316
    • Psihoyios, G.1    Simos, T.E.2
  • 29
    • 17744365569 scopus 로고    scopus 로고
    • A family of multiderivative methods for the numerical solution of the Schrödinger equation
    • Sakas D. P., Simos T. E.: A family of multiderivative methods for the numerical solution of the Schrödinger equation. J. Math. Chem. 37(3), 317-331 (2005).
    • (2005) J. Math. Chem. , vol.37 , Issue.3 , pp. 317-331
    • Sakas, D.P.1    Simos, T.E.2
  • 30
    • 3543013740 scopus 로고    scopus 로고
    • Exponentially-fitted multiderivative methods for the numerical solution of the Schrödinger equation
    • Simos T. E.: Exponentially-fitted multiderivative methods for the numerical solution of the Schrödinger equation. J. Math. Chem. 36(1), 13-27 (2004).
    • (2004) J. Math. Chem. , vol.36 , Issue.1 , pp. 13-27
    • Simos, T.E.1
  • 31
    • 3542994480 scopus 로고    scopus 로고
    • Symplectic methods of fifth order for the numerical solution of the radial Shrodinger equation
    • Tselios K., Simos T. E.: Symplectic methods of fifth order for the numerical solution of the radial Shrodinger equation. J. Math. Chem. 35(1), 55-63 (2004).
    • (2004) J. Math. Chem. , vol.35 , Issue.1 , pp. 55-63
    • Tselios, K.1    Simos, T.E.2
  • 32
    • 1642456496 scopus 로고    scopus 로고
    • A family of trigonometrically-fitted symmetric methods for the efficient solution of the Schrödinger equation and related problems
    • Simos T. E.: A family of trigonometrically-fitted symmetric methods for the efficient solution of the Schrödinger equation and related problems. J. Math. Chem. 34(1-2), 39-58 (2003).
    • (2003) J. Math. Chem. , vol.34 , Issue.1-2 , pp. 39-58
    • Simos, T.E.1
  • 33
    • 1642456494 scopus 로고    scopus 로고
    • Symplectic methods for the numerical solution of the radial Shrödinger equation
    • Tselios K., Simos T. E.: Symplectic methods for the numerical solution of the radial Shrödinger equation. J. Math. Chem. 34(1-2), 83-94 (2003).
    • (2003) J. Math. Chem. , vol.34 , Issue.1-2 , pp. 83-94
    • Tselios, K.1    Simos, T.E.2
  • 34
    • 0141831831 scopus 로고    scopus 로고
    • Family of twelve steps exponential fitting symmetric multistep methods for the numerical solution of the Schrödinger equation
    • Vigo-Aguiar J J., Simos T. E.: Family of twelve steps exponential fitting symmetric multistep methods for the numerical solution of the Schrödinger equation. J. Math. Chem. 32(3), 257-270 (2002).
    • (2002) J. Math. Chem. , vol.32 , Issue.3 , pp. 257-270
    • Vigo-Aguiar, J.J.1    Simos, T.E.2
  • 35
    • 0141608674 scopus 로고    scopus 로고
    • New P-stable eighth algebraic order exponentially-fitted methods for the numerical integration of the Schrödinger equation
    • Avdelas G., Kefalidis E., Simos T. E.: New P-stable eighth algebraic order exponentially-fitted methods for the numerical integration of the Schrödinger equation. J. Math. Chem. 31(4), 371-404 (2002).
    • (2002) J. Math. Chem. , vol.31 , Issue.4 , pp. 371-404
    • Avdelas, G.1    Kefalidis, E.2    Simos, T.E.3
  • 36
    • 0036485707 scopus 로고    scopus 로고
    • Symmetric eighth algebraic order methods with minimal phase-lag for the numerical solution of the Schrödinger equation
    • Simos T. E., Vigo-Aguiar J.: Symmetric eighth algebraic order methods with minimal phase-lag for the numerical solution of the Schrödinger equation. J. Math. Chem. 31(2), 135-144 (2002).
    • (2002) J. Math. Chem. , vol.31 , Issue.2 , pp. 135-144
    • Simos, T.E.1    Vigo-Aguiar, J.2
  • 37
    • 0036485703 scopus 로고    scopus 로고
    • Construction of trigonometrically and exponentially fitted Runge-Kutta-Nystrom methods for the numerical solution of the Schrödinger equation and related problems a method of 8th algebraic order
    • Z. Kalogiratou, T. E. Simos, Construction of trigonometrically and exponentially fitted Runge-Kutta-Nystrom methods for the numerical solution of the Schrödinger equation and related problems a method of 8th algebraic order. J. Math. Chem. 31(2): 211-232.
    • J. Math. Chem. , vol.31 , Issue.1 , pp. 121-131
    • Kalogiratou, Z.1    Simos, T.E.2
  • 38
    • 0035384934 scopus 로고    scopus 로고
    • A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation
    • Simos T. E., Vigo-Aguiar J.: A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation. J. Math. Chem. 30(1), 121-131 (2001).
    • (2001) J. Math. Chem. , vol.30 , Issue.1 , pp. 121-131
    • Simos, T.E.1    Vigo-Aguiar, J.2
  • 39
    • 0035539374 scopus 로고    scopus 로고
    • A generator and an optimized generator of high-order hybrid explicit methods for the numerical solution of the Schrödinger equation. Part 1. Development of the basic method
    • Avdelas G., Konguetsof A., Simos T. E.: A generator and an optimized generator of high-order hybrid explicit methods for the numerical solution of the Schrödinger equation. Part 1. Development of the basic method. J. Math. Chem. 29(4), 281-291 (2001).
    • (2001) J. Math. Chem. , vol.29 , Issue.4 , pp. 281-291
    • Avdelas, G.1    Konguetsof, A.2    Simos, T.E.3
  • 40
    • 0035539372 scopus 로고    scopus 로고
    • A generator and an optimized generator of high-order hybrid explicit methods for the numerical solution of the Schrödinger equation. Part 2. Development of the generator; optimization of the generator and numerical results
    • Avdelas G., Konguetsof A., Simos T. E.: A generator and an optimized generator of high-order hybrid explicit methods for the numerical solution of the Schrödinger equation. Part 2. Development of the generator; optimization of the generator and numerical results. J. Math. Chem. 29(4), 293-305 (2001).
    • (2001) J. Math. Chem. , vol.29 , Issue.4 , pp. 293-305
    • Avdelas, G.1    Konguetsof, A.2    Simos, T.E.3
  • 41
    • 0035315407 scopus 로고    scopus 로고
    • A family of P-stable eighth algebraic order methods with exponential fitting facilities
    • Vigo-Aguiar J., Simos T. E.: A family of P-stable eighth algebraic order methods with exponential fitting facilities. J. Math. Chem. 29(3), 177-189 (2001).
    • (2001) J. Math. Chem. , vol.29 , Issue.3 , pp. 177-189
    • Vigo-Aguiar, J.1    Simos, T.E.2
  • 42
    • 0034338028 scopus 로고    scopus 로고
    • A new explicit Bessel and Neumann fitted eighth algebraic order method for the numerical solution of the Schrödinger equation
    • Simos T. E.: A new explicit Bessel and Neumann fitted eighth algebraic order method for the numerical solution of the Schrödinger equation. J. Math. Chem. 27(4), 343-356 (2000).
    • (2000) J. Math. Chem. , vol.27 , Issue.4 , pp. 343-356
    • Simos, T.E.1
  • 43
    • 0033114512 scopus 로고    scopus 로고
    • Embedded eighth order methods for the numerical solution of the Schrödinger equation
    • Avdelas G., Simos T. E.: Embedded eighth order methods for the numerical solution of the Schrödinger equation. J. Math. Chem. 26(4), 327-341 (1999).
    • (1999) J. Math. Chem. , vol.26 , Issue.4 , pp. 327-341
    • Avdelas, G.1    Simos, T.E.2
  • 44
    • 0033429763 scopus 로고    scopus 로고
    • A family of P-stable exponentially-fitted methods for the numerical solution of the Schrödinger equation
    • Simos T. E.: A family of P-stable exponentially-fitted methods for the numerical solution of the Schrödinger equation. J. Math. Chem. 25(1), 65-84 (1999).
    • (1999) J. Math. Chem. , vol.25 , Issue.1 , pp. 65-84
    • Simos, T.E.1
  • 45
    • 0039065106 scopus 로고    scopus 로고
    • Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations
    • Simos T. E.: Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations. J. Math. Chem. 24(1-3), 23-37 (1998).
    • (1998) J. Math. Chem. , vol.24 , Issue.1-3 , pp. 23-37
    • Simos, T.E.1
  • 46
    • 0031326292 scopus 로고    scopus 로고
    • Eighth order methods with minimal phase-lag for accurate computations for the elastic scattering phase-shift problem
    • Simos T. E.: Eighth order methods with minimal phase-lag for accurate computations for the elastic scattering phase-shift problem. J. Math. Chem. 21(4), 359-372 (1997).
    • (1997) J. Math. Chem. , vol.21 , Issue.4 , pp. 359-372
    • Simos, T.E.1
  • 47
    • 67650601032 scopus 로고    scopus 로고
    • Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions
    • Panopoulos G. A., Anastassi Z. A., Simos T. E.: Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions. J. Math. Chem. 46(2), 604-620 (2009).
    • (2009) J. Math. Chem. , vol.46 , Issue.2 , pp. 604-620
    • Panopoulos, G.A.1    Anastassi, Z.A.2    Simos, T.E.3
  • 48
    • 63049137270 scopus 로고    scopus 로고
    • A family of two-stage two-step methods for the numerical integration of the Schrödinger equation and related IVPs with oscillating solution
    • Anastassi Z. A., Simos T. E.: A family of two-stage two-step methods for the numerical integration of the Schrödinger equation and related IVPs with oscillating solution. J. Math. Chem. 45(4), 1102-1129 (2009).
    • (2009) J. Math. Chem. , vol.45 , Issue.4 , pp. 1102-1129
    • Anastassi, Z.A.1    Simos, T.E.2
  • 49
    • 48349083727 scopus 로고    scopus 로고
    • A family of four-step trigonometrically-fitted methods and its application to the schrodinger equation
    • Simos T. E.: A family of four-step trigonometrically-fitted methods and its application to the schrodinger equation. J. Math. Chem. 44(2), 447-466 (2009).
    • (2009) J. Math. Chem. , vol.44 , Issue.2 , pp. 447-466
    • Simos, T.E.1
  • 50
    • 48349089428 scopus 로고    scopus 로고
    • Closed Newton-Cotes trigonometrically-fitted formulae of high order for the numerical integration of the Schrödinger equation
    • Simos T. E.: Closed Newton-Cotes trigonometrically-fitted formulae of high order for the numerical integration of the Schrödinger equation. J. Math. Chem. 44(2), 483-499 (2008).
    • (2008) J. Math. Chem. , vol.44 , Issue.2 , pp. 483-499
    • Simos, T.E.1
  • 51
    • 34548440749 scopus 로고    scopus 로고
    • New second-order exponentially and trigonometrically fitted symplectic integrators for the numerical solution of the time-independent Schrödinger equation
    • Monovasilis T., Simos T. E.: New second-order exponentially and trigonometrically fitted symplectic integrators for the numerical solution of the time-independent Schrödinger equation. J. Math. Chem. 42(3), 535-545 (2007).
    • (2007) J. Math. Chem. , vol.42 , Issue.3 , pp. 535-545
    • Monovasilis, T.1    Simos, T.E.2
  • 52
    • 58149236704 scopus 로고    scopus 로고
    • New trigonometrically fitted six-step symmetric methods for the efficient solution of the Schrödinger equation
    • Anastassi Z. A., Simos T. E.: New trigonometrically fitted six-step symmetric methods for the efficient solution of the Schrödinger equation. Match-Commun. Math. Comput. Chem. 60(3), 733-752 (2008).
    • (2008) Match-Commun. Math. Comput. Chem. , vol.60 , Issue.3 , pp. 733-752
    • Anastassi, Z.A.1    Simos, T.E.2
  • 53
    • 58149229321 scopus 로고    scopus 로고
    • Two optimized Runge-Kutta methods for the solution of the Schrödinger equation
    • Triantafyllidis T. V., Anastassi Z. A., Simos T. E.: Two optimized Runge-Kutta methods for the solution of the Schrödinger equation. Match-Commun. Math. Comput. Chem. 60(3), 753-771 (2008).
    • (2008) Match-Commun. Math. Comput. Chem. , vol.60 , Issue.3 , pp. 753-771
    • Triantafyllidis, T.V.1    Anastassi, Z.A.2    Simos, T.E.3
  • 54
    • 54049139508 scopus 로고    scopus 로고
    • Two new optimized eight-step symmetric methods for the efficient solution of the Schrödinger equation and related problems
    • Panopoulos G. A., Anastassi Z. A., Simos T. E.: Two new optimized eight-step symmetric methods for the efficient solution of the Schrödinger equation and related problems. Match-Commun. Math. Comput. Chem. 60(3), 773-785 (2008).
    • (2008) Match-Commun. Math. Comput. Chem. , vol.60 , Issue.3 , pp. 773-785
    • Panopoulos, G.A.1    Anastassi, Z.A.2    Simos, T.E.3
  • 55
    • 58149234013 scopus 로고    scopus 로고
    • Closed Newton-Cotes trigonometrically-fitted formulae for the solution of the Schrödinger equation
    • Simos T. E.: Closed Newton-Cotes trigonometrically-fitted formulae for the solution of the Schrödinger equation. Match-Commun. Math. Comput. Chem. 60(3), 787-801 (2008).
    • (2008) Match-Commun. Math. Comput. Chem. , vol.60 , Issue.3 , pp. 787-801
    • Simos, T.E.1
  • 56
    • 58149247938 scopus 로고    scopus 로고
    • A six-step P-stable trigonometrically-fitted method for the numerical integration of the radial Schrödinger equation
    • Anastassi Z. A., Simos T. E.: A six-step P-stable trigonometrically-fitted method for the numerical integration of the radial Schrödinger equation. Match-Commun. Math. Comput. Chem. 60(3), 803-830 (2008).
    • (2008) Match-Commun. Math. Comput. Chem. , vol.60 , Issue.3 , pp. 803-830
    • Anastassi, Z.A.1    Simos, T.E.2
  • 57
    • 27544444096 scopus 로고    scopus 로고
    • Trigonometrically-fitted multiderivative methods for the numerical solution of the radial Schrödinger equation
    • Sakas D. P., Simos T. E.: Trigonometrically-fitted multiderivative methods for the numerical solution of the radial Schrödinger equation. Match-Commun. Math. Comput. Chem. 53(2), 299-320 (2005).
    • (2005) Match-Commun. Math. Comput. Chem. , vol.53 , Issue.2 , pp. 299-320
    • Sakas, D.P.1    Simos, T.E.2
  • 58
    • 17744366054 scopus 로고    scopus 로고
    • A family of fifth algebraic order trigonometrically fitted P-C schemes for the numerical solution of the radial Schrödinger equation
    • Psihoyios G., Simos T. E.: A family of fifth algebraic order trigonometrically fitted P-C schemes for the numerical solution of the radial Schrödinger equation. Match-Commun. Math. Comput. Chem. 53(2), 321-344 (2005).
    • (2005) Match-Commun. Math. Comput. Chem. , vol.53 , Issue.2 , pp. 321-344
    • Psihoyios, G.1    Simos, T.E.2
  • 60
    • 33846400845 scopus 로고    scopus 로고
    • Lobatto-Obrechkoff formulae for 2nd order two-point boundary value problems
    • Capper S. D., Cash J. R., Moore D. R.: Lobatto-Obrechkoff formulae for 2nd order two-point boundary value problems. JNAIAM J. Numer. Anal. Indust. Appl. Math. 1(1), 13-25 (2006).
    • (2006) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.1 , Issue.1 , pp. 13-25
    • Capper, S.D.1    Cash, J.R.2    Moore, D.R.3
  • 61
  • 63
    • 84946899933 scopus 로고    scopus 로고
    • Variable step Runge-Kutta-Nystrom methods for the numerical solution of reversible systems
    • Cash J. R., Girdlestone S.: Variable step Runge-Kutta-Nystrom methods for the numerical solution of reversible systems. JNAIAM J. Numer. Anal. Indust. Appl. Math. 1(1), 59-80 (2006).
    • (2006) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.1 , Issue.1 , pp. 59-80
    • Cash, J.R.1    Girdlestone, S.2
  • 64
    • 48349113977 scopus 로고    scopus 로고
    • Hybrid mesh selection algorithms based on conditioning for two-point boundary value problems
    • Cash J. R., Mazzia F.: Hybrid mesh selection algorithms based on conditioning for two-point boundary value problems. JNAIAM J. Numer. Anal. Indust. Appl. Math. 1(1), 81-90 (2006).
    • (2006) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.1 , Issue.1 , pp. 81-90
    • Cash, J.R.1    Mazzia, F.2
  • 66
    • 35348858669 scopus 로고    scopus 로고
    • Discrete conservative vector fields induced by the trapezoidal method
    • Iavernaro F., Trigiante D.: Discrete conservative vector fields induced by the trapezoidal method. JNAIAM J. Numer. Anal. Indust. Appl. Math. 1(1), 113-130 (2006).
    • (2006) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.1 , Issue.1 , pp. 113-130
    • Iavernaro, F.1    Trigiante, D.2
  • 70
  • 72
    • 58249084274 scopus 로고    scopus 로고
    • Embedding a general-purpose numerical library in an interactive environment
    • Dewar M.: Embedding a general-purpose numerical library in an interactive environment. JNAIAM J. Numer. Anal. Indust. Appl. Math. 3, 17-26 (2008).
    • (2008) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.3 , pp. 17-26
    • Dewar, M.1
  • 75
    • 67349205394 scopus 로고    scopus 로고
    • Solving differential algebraic equations by Taylor series (III): The DAETS code
    • Nedialkov N. S., Pryce J. D.: Solving differential algebraic equations by Taylor series (III): the DAETS code. JNAIAM J. Numer. Anal. Indust. Appl. Math. 3, 61-80 (2008).
    • (2008) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.3 , pp. 61-80
    • Nedialkov, N.S.1    Pryce, J.D.2
  • 76
    • 67650640459 scopus 로고    scopus 로고
    • The SCHOL Project at the University of Maryland: Using mathematical software in the teaching of Sophomore differential equations
    • Lipsman R. L., Osborn J. E., Rosenberg J. M.: The SCHOL Project at the University of Maryland: using mathematical software in the teaching of Sophomore differential equations. JNAIAM J. Numer. Anal. Indust. Appl. Math. 3, 81-103 (2008).
    • (2008) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.3 , pp. 81-103
    • Lipsman, R.L.1    Osborn, J.E.2    Rosenberg, J.M.3
  • 78
    • 67650631080 scopus 로고    scopus 로고
    • PythNon: A PSE for the numerical solution of nonlinear algebraic equations
    • Spiteri R. J., Ter Thian-Peng: pythNon: a PSE for the numerical solution of nonlinear algebraic equations. JNAIAM J. Numer. Anal. Indust. Appl. Math. 3, 123-137 (2008).
    • (2008) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.3 , pp. 123-137
    • Spiteri, R.J.1    Ter, T.-P.2
  • 81
    • 67650646714 scopus 로고    scopus 로고
    • Automatic code generation and optimization in maple
    • Wittkopf A.: Automatic code generation and optimization in maple. JNAIAM J. Numer. Anal. Indust. Appl. Math. 3, 167-180 (2008).
    • (2008) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.3 , pp. 167-180
    • Wittkopf, A.1
  • 83
    • 67650691142 scopus 로고    scopus 로고
    • Simulation and inversion of seismic wave propagation on continental scales based on a spectral-element method
    • Fichtner A., Igel H., Bunge H.-P., Kennett B. L. N.: Simulation and inversion of seismic wave propagation on continental scales based on a spectral-element method. JNAIAM J. Numer. Anal. Indust. Appl. Math. 4, 11-22 (2009).
    • (2009) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.4 , pp. 11-22
    • Fichtner, A.1    Igel, H.2    Bunge, H.-P.3    Kennett, B.L.N.4
  • 84
    • 67650652513 scopus 로고    scopus 로고
    • Blended general linear methods based on boundary value methods in the generalized BDF family
    • Brugnano L., Magherini C.: Blended general linear methods based on boundary value methods in the generalized BDF family. JNAIAM J. Numer. Anal. Indust. Appl. Math. 4, 23-40 (2009).
    • (2009) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.4 , pp. 23-40
    • Brugnano, L.1    Magherini, C.2
  • 85
    • 67650668034 scopus 로고    scopus 로고
    • Spectral approximation of time windows in the solution of dissipative linear differential equations
    • Burrage K., Jackiewicz Z., Welfert B. D.: Spectral approximation of time windows in the solution of dissipative linear differential equations. JNAIAM J. Numer. Anal. Indust. Appl. Math. 4, 41-64 (2009).
    • (2009) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.4 , pp. 41-64
    • Burrage, K.1    Jackiewicz, Z.2    Welfert, B.D.3
  • 86
    • 67650652507 scopus 로고    scopus 로고
    • Variable step/order generalized upwind methods for the numerical solution of second order singular perturbation problems
    • Amodio P., Settanni G.: Variable step/order generalized upwind methods for the numerical solution of second order singular perturbation problems. JNAIAM J. Numer. Anal. Indust. Appl. Math. 4, 65-76 (2009).
    • (2009) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.4 , pp. 65-76
    • Amodio, P.1    Settanni, G.2
  • 88
    • 67650694301 scopus 로고    scopus 로고
    • High-order symmetric schemes for the energy conservation of polynomial Hamiltonian problems
    • Iavernaro F., Trigiante D.: High-order symmetric schemes for the energy conservation of polynomial Hamiltonian problems. JNAIAM J. Numer. Anal. Indust. Appl. Math. 4, 87-101 (2009).
    • (2009) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.4 , pp. 87-101
    • Iavernaro, F.1    Trigiante, D.2
  • 89
    • 67650686107 scopus 로고    scopus 로고
    • Linear multistep approximation of nonsymmetric rotating systems
    • Hill A. T.: Linear multistep approximation of nonsymmetric rotating systems. JNAIAM J. Numer. Anal. Indust. Appl. Math. 4, 103-112 (2009).
    • (2009) JNAIAM J. Numer. Anal. Indust. Appl. Math. , vol.4 , pp. 103-112
    • Hill, A.T.1
  • 92
    • 33846374833 scopus 로고    scopus 로고
    • A block implicit advanced step-point (BIAS) algorithm for stiff differential systems
    • Psihoyios G.: A block implicit advanced step-point (BIAS) algorithm for stiff differential systems. Comput Lett 2(1-2), 51-58 (2006).
    • (2006) Comput Lett , vol.2 , Issue.1-2 , pp. 51-58
    • Psihoyios, G.1
  • 93
    • 48349127709 scopus 로고    scopus 로고
    • On the use of 'arc length' and 'defect' for mesh selection for differential equations
    • Enright W. H.: On the use of 'arc length' and 'defect' for mesh selection for differential equations. Comput Lett 1(2), 47-52 (2005).
    • (2005) Comput Lett , vol.1 , Issue.2 , pp. 47-52
    • Enright, W.H.1
  • 94
    • 30344464634 scopus 로고    scopus 로고
    • P-stable four-step exponentially-fitted method for the numerical integration of the Schrödinger equation
    • Simos T. E.: P-stable four-step exponentially-fitted method for the numerical integration of the Schrödinger equation. Comput. Lett. 1(1), 37-45 (2005).
    • (2005) Comput. Lett. , vol.1 , Issue.1 , pp. 37-45
    • Simos, T.E.1
  • 95
    • 34249905635 scopus 로고    scopus 로고
    • Stabilization of a four-step exponentially-fitted method and its application to the Schrödinger equation
    • Simos T. E.: Stabilization of a four-step exponentially-fitted method and its application to the Schrödinger equation. Int. J. Modern Phys. C 18(3), 315-328 (2007).
    • (2007) Int. J. Modern Phys. C , vol.18 , Issue.3 , pp. 315-328
    • Simos, T.E.1
  • 96
    • 24644444204 scopus 로고    scopus 로고
    • P-stable linear symmetric multistep methods for periodic initial-value problems
    • Wang Z.: P-stable linear symmetric multistep methods for periodic initial-value problems. Comput. Phys. Commun. 171, 162-174 (2005).
    • (2005) Comput. Phys. Commun. , vol.171 , pp. 162-174
    • Wang, Z.1
  • 97
    • 27944475127 scopus 로고
    • A Runge-Kutta Fehlberg method with phase-lag of order infinity for initial value problems with oscillating solution
    • Simos T. E.: A Runge-Kutta Fehlberg method with phase-lag of order infinity for initial value problems with oscillating solution. Comput. Math. Appl. 25, 95-101 (1993).
    • (1993) Comput. Math. Appl. , vol.25 , pp. 95-101
    • Simos, T.E.1
  • 98
    • 0002659592 scopus 로고
    • Runge-Kutta interpolants with minimal phase-lag
    • Simos T. E.: Runge-Kutta interpolants with minimal phase-lag. Comput. Math. Appl. 26, 43-49 (1993).
    • (1993) Comput. Math. Appl. , vol.26 , pp. 43-49
    • Simos, T.E.1
  • 99
    • 0041934483 scopus 로고
    • Runge-Kutta-Nyström interpolants for the numerical integration of special second-order periodic initial-value problems
    • Simos T. E.: Runge-Kutta-Nyström interpolants for the numerical integration of special second-order periodic initial-value problems. Comput. Math. Appl. 26, 7-15 (1993).
    • (1993) Comput. Math. Appl. , vol.26 , pp. 7-15
    • Simos, T.E.1
  • 100
    • 0005239360 scopus 로고
    • A family of four-step exponential fitted methods for the numerical integration of the radial Schrödinger equation
    • Simos T. E., Mitsou G. V.: A family of four-step exponential fitted methods for the numerical integration of the radial Schrödinger equation. Comput. Math. Appl. 28, 41-50 (1994).
    • (1994) Comput. Math. Appl. , vol.28 , pp. 41-50
    • Simos, T.E.1    Mitsou, G.V.2
  • 101
    • 0001067740 scopus 로고
    • A two-step method for the numerical solution of the radial Schrodinger equation
    • Simos T. E., Mousadis G.: A two-step method for the numerical solution of the radial Schrodinger equation. Comput. Math. Appl. 29, 31-37 (1995).
    • (1995) Comput. Math. Appl. , vol.29 , pp. 31-37
    • Simos, T.E.1    Mousadis, G.2
  • 102
    • 0002763998 scopus 로고    scopus 로고
    • Block Runge-Kutta methods for periodic initial-value problems
    • Avdelas G., Simos T. E.: Block Runge-Kutta methods for periodic initial-value problems. Comput. Math. Appl. 31, 69-83 (1996).
    • (1996) Comput. Math. Appl. , vol.31 , pp. 69-83
    • Avdelas, G.1    Simos, T.E.2
  • 103
    • 0002207932 scopus 로고    scopus 로고
    • Embedded methods for the numerical solution of the Schrödinger equation
    • Avdelas G., Simos T. E.: Embedded methods for the numerical solution of the Schrödinger equation. Comput. Math. Appl. 31, 85-102 (1996).
    • (1996) Comput. Math. Appl. , vol.31 , pp. 85-102
    • Avdelas, G.1    Simos, T.E.2
  • 104
    • 0030291643 scopus 로고    scopus 로고
    • A new method for the numerical solution of fourth order BVP with oscillating solutions
    • Papakaliatakis G., Simos T. E.: A new method for the numerical solution of fourth order BVP with oscillating solutions. Comput. Math. Appl. 32, 1-6 (1996).
    • (1996) Comput. Math. Appl. , vol.32 , pp. 1-6
    • Papakaliatakis, G.1    Simos, T.E.2
  • 105
    • 0031128552 scopus 로고    scopus 로고
    • An extended Numerov-type method for the numerical solution of the Schrödinger equation
    • Simos T. E.: An extended Numerov-type method for the numerical solution of the Schrödinger equation. Comput. Math. Appl. 33, 67-78 (1997).
    • (1997) Comput. Math. Appl. , vol.33 , pp. 67-78
    • Simos, T.E.1
  • 106
    • 0032117901 scopus 로고    scopus 로고
    • A new hybrid imbedded variable-step procedure for the numerical integration of the Schrödinger equation
    • Simos T. E.: A new hybrid imbedded variable-step procedure for the numerical integration of the Schrödinger equation. Comput. Math. Appl. 36, 51-63 (1998).
    • (1998) Comput. Math. Appl. , vol.36 , pp. 51-63
    • Simos, T.E.1
  • 107
    • 0035452056 scopus 로고    scopus 로고
    • Bessel and Neumann fitted methods for the numerical solution of the Schrödinger equation
    • Simos T. E.: Bessel and Neumann fitted methods for the numerical solution of the Schrödinger equation. Comput. Math. Appl. 42, 833-847 (2001).
    • (2001) Comput. Math. Appl. , vol.42 , pp. 833-847
    • Simos, T.E.1
  • 108
    • 0037282210 scopus 로고    scopus 로고
    • An exponentially-fitted and trigonometrically-fitted method for the numerical solution of periodic initial-value problems
    • Konguetsof A., Simos T. E.: An exponentially-fitted and trigonometrically-fitted method for the numerical solution of periodic initial-value problems. Comput. Math. Appl. 45, 547-554 (2003).
    • (2003) Comput. Math. Appl. , vol.45 , pp. 547-554
    • Konguetsof, A.1    Simos, T.E.2
  • 109
    • 11044230429 scopus 로고    scopus 로고
    • An optimized Runge-Kutta method for the solution of orbital problems
    • Anastassi Z. A., Simos T. E.: An optimized Runge-Kutta method for the solution of orbital problems. J. Comput. Appl. Math. 175(1), 1-9 (2005).
    • (2005) J. Comput. Appl. Math. , vol.175 , Issue.1 , pp. 1-9
    • Anastassi, Z.A.1    Simos, T.E.2
  • 110
    • 11044230652 scopus 로고    scopus 로고
    • A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions
    • Psihoyios G., Simos T. E.: A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions. J. Comput. Appl. Math. 175(1), 137-147 (2005).
    • (2005) J. Comput. Appl. Math. , vol.175 , Issue.1 , pp. 137-147
    • Psihoyios, G.1    Simos, T.E.2
  • 111
    • 11044223038 scopus 로고    scopus 로고
    • Multiderivative methods of eighth algrebraic order with minimal phase-lag for the numerical solution of the radial Schrödinger equation
    • Sakas D. P., Simos T. E.: Multiderivative methods of eighth algrebraic order with minimal phase-lag for the numerical solution of the radial Schrödinger equation. J. Comput. Appl. Math. 175(1), 161-172 (2005).
    • (2005) J. Comput. Appl. Math. , vol.175 , Issue.1 , pp. 161-172
    • Sakas, D.P.1    Simos, T.E.2
  • 112
    • 11044225131 scopus 로고    scopus 로고
    • Runge-Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics
    • Tselios K., Simos T. E.: Runge-Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics. J. Comput. Appl. Math. 175(1), 173-181 (2005).
    • (2005) J. Comput. Appl. Math. , vol.175 , Issue.1 , pp. 173-181
    • Tselios, K.1    Simos, T.E.2
  • 113
    • 0042785955 scopus 로고    scopus 로고
    • Newton-Cotes formulae for long-time integration
    • Kalogiratou Z., Simos T. E.: Newton-Cotes formulae for long-time integration. J. Comput. Appl. Math. 158(1), 75-82 (2003).
    • (2003) J. Comput. Appl. Math. , vol.158 , Issue.1 , pp. 75-82
    • Kalogiratou, Z.1    Simos, T.E.2
  • 114
    • 0042284832 scopus 로고    scopus 로고
    • Symplectic integrators for the numerical solution of the Schrödinger equation
    • Kalogiratou Z., Monovasilis T., Simos T. E.: Symplectic integrators for the numerical solution of the Schrödinger equation. J. Comput. Appl. Math. 158(1), 83-92 (2003).
    • (2003) J. Comput. Appl. Math. , vol.158 , Issue.1 , pp. 83-92
    • Kalogiratou, Z.1    Monovasilis, T.2    Simos, T.E.3
  • 115
    • 0042785945 scopus 로고    scopus 로고
    • A generator of hybrid symmetric four-step methods for the numerical solution of the Schrödinger equation
    • Konguetsof A., Simos T. E.: A generator of hybrid symmetric four-step methods for the numerical solution of the Schrödinger equation. J. Comput. Appl. Math. 158(1), 93-106 (2003).
    • (2003) J. Comput. Appl. Math. , vol.158 , Issue.1 , pp. 93-106
    • Konguetsof, A.1    Simos, T.E.2
  • 116
    • 0043287096 scopus 로고    scopus 로고
    • Trigonometrically fitted predictor-corrector methods for IVPs with oscillating solutions
    • Psihoyios G., Simos T. E.: Trigonometrically fitted predictor-corrector methods for IVPs with oscillating solutions. J. Comput. Appl. Math. 158(1), 135-144 (2003).
    • (2003) J. Comput. Appl. Math. , vol.158 , Issue.1 , pp. 135-144
    • Psihoyios, G.1    Simos, T.E.2
  • 117
    • 0037109217 scopus 로고    scopus 로고
    • Optimized Runge-Kutta pairs for problems with oscillating solutions
    • Tsitouras C., Simos T. E.: Optimized Runge-Kutta pairs for problems with oscillating solutions. J. Comput. Appl. Math. 147(2), 397-409 (2002).
    • (2002) J. Comput. Appl. Math. , vol.147 , Issue.2 , pp. 397-409
    • Tsitouras, C.1    Simos, T.E.2
  • 118
    • 0032842252 scopus 로고    scopus 로고
    • An exponentially fitted eighth-order method for the numerical solution of the Schrödinger equation
    • Simos T. E.: An exponentially fitted eighth-order method for the numerical solution of the Schrödinger equation. J. Comput. Appl. Math. 108(1-2), 177-194 (1999).
    • (1999) J. Comput. Appl. Math. , vol.108 , Issue.1-2 , pp. 177-194
    • Simos, T.E.1
  • 119
    • 0032048272 scopus 로고    scopus 로고
    • An accurate finite difference method for the numerical solution of the Schrödinger equation
    • Simos T. E.: An accurate finite difference method for the numerical solution of the Schrödinger equation. J. Comput. Appl. Math. 91(1), 47-61 (1998).
    • (1998) J. Comput. Appl. Math. , vol.91 , Issue.1 , pp. 47-61
    • Simos, T.E.1
  • 120
    • 0031357296 scopus 로고    scopus 로고
    • A family of hybrid exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrödinger equation
    • Thomas R. M., Simos T. E.: A family of hybrid exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrödinger equation. J. Comput. Appl. Math. 87(2), 215-226 (1997).
    • (1997) J. Comput. Appl. Math. , vol.87 , Issue.2 , pp. 215-226
    • Thomas, R.M.1    Simos, T.E.2
  • 121
    • 0031101965 scopus 로고    scopus 로고
    • A finite-difference method for the numerical solution of the Schrödinger equation
    • Simos T. E., Williams P. S.: A finite-difference method for the numerical solution of the Schrödinger equation. J. Comput. Appl. Math. 79(2), 189-205 (1997).
    • (1997) J. Comput. Appl. Math. , vol.79 , Issue.2 , pp. 189-205
    • Simos, T.E.1    Williams, P.S.2
  • 122
    • 0030211501 scopus 로고    scopus 로고
    • A generator of high-order embedded P-stable methods for the numerical solution of the Schrödinger equation
    • Avdelas G., Simos T. E.: A generator of high-order embedded P-stable methods for the numerical solution of the Schrödinger equation. J. Comput. Appl. Math. 72(2), 345-358 (1996).
    • (1996) J. Comput. Appl. Math. , vol.72 , Issue.2 , pp. 345-358
    • Avdelas, G.1    Simos, T.E.2
  • 123
    • 0030103209 scopus 로고    scopus 로고
    • A family of Numerov-type exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrödinger equation
    • Thomas R. M., Simos T. E., Mitsou G. V.: A family of Numerov-type exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrödinger equation. J. Comput. Appl. Math. 67(2), 255-270 (1996).
    • (1996) J. Comput. Appl. Math. , vol.67 , Issue.2 , pp. 255-270
    • Thomas, R.M.1    Simos, T.E.2    Mitsou, G.V.3
  • 124
    • 0043103462 scopus 로고
    • A family of 4-step exponentially fitted predictor-corrector methods for the numerical-integration of the Schrödinger-equation
    • Simos T. E.: A family of 4-step exponentially fitted predictor-corrector methods for the numerical-integration of the Schrödinger-equation. J. Comput. Appl. Math. 58(3), 337-344 (1995).
    • (1995) J. Comput. Appl. Math. , vol.58 , Issue.3 , pp. 337-344
    • Simos, T.E.1
  • 125
    • 0041738853 scopus 로고
    • An explicit 4-step phase-fitted method for the numerical-integration of 2nd-order initial-value problems
    • Simos T. E.: An explicit 4-step phase-fitted method for the numerical-integration of 2nd-order initial-value problems. J. Comput. Appl. Math. 55(2), 125-133 (1994).
    • (1994) J. Comput. Appl. Math. , vol.55 , Issue.2 , pp. 125-133
    • Simos, T.E.1
  • 126
    • 0001499606 scopus 로고
    • A Runge-Kutta-Nyström method for the numerical-integration of special 2nd-order periodic initial-value problems
    • Simos T. E., Dimas E., Sideridis A. B.: A Runge-Kutta-Nyström method for the numerical-integration of special 2nd-order periodic initial-value problems. J. Comput. Appl. Math. 51(3), 317-326 (1994).
    • (1994) J. Comput. Appl. Math. , vol.51 , Issue.3 , pp. 317-326
    • Simos, T.E.1    Dimas, E.2    Sideridis, A.B.3
  • 127
    • 38249009386 scopus 로고
    • A low-order embedded Runge-Kutta method for periodic initial-value problems
    • Sideridis A. B., Simos T. E.: A low-order embedded Runge-Kutta method for periodic initial-value problems. J. Comput. Appl. Math. 44(2), 235-244 (1992).
    • (1992) J. Comput. Appl. Math. , vol.44 , Issue.2 , pp. 235-244
    • Sideridis, A.B.1    Simos, T.E.2
  • 128
    • 0001515713 scopus 로고
    • A 4th-order Bessel fitting method for the numerical-solution of the SchrÖdinger-equation
    • Simos T. E., amd Raptis A. D.: A 4th-order Bessel fitting method for the numerical-solution of the SchrÖdinger-equation. J. Comput. Appl. Math. 43(3), 313-322 (1992).
    • (1992) J. Comput. Appl. Math. , vol.43 , Issue.3 , pp. 313-322
    • Simos, T.E.1    Amd, R.A.D.2
  • 129
    • 0002586288 scopus 로고
    • Explicit 2-step methods with minimal phase-lag for the numerical-integration of special 2nd-order initial-value problems and their application to the one-dimensional Schrödinger-equation
    • Simos T. E.: Explicit 2-step methods with minimal phase-lag for the numerical-integration of special 2nd-order initial-value problems and their application to the one-dimensional Schrödinger-equation. J. Comput. Appl. Math. 39(1), 89-94 (1992).
    • (1992) J. Comput. Appl. Math. , vol.39 , Issue.1 , pp. 89-94
    • Simos, T.E.1
  • 130
    • 0000168727 scopus 로고
    • A 4-step method for the numerical-solution of the Schrödinger-equation
    • Simos T. E.: A 4-step method for the numerical-solution of the Schrödinger-equation. J. Comput. Appl. Math. 30(3), 251-255 (1990).
    • (1990) J. Comput. Appl. Math. , vol.30 , Issue.3 , pp. 251-255
    • Simos, T.E.1
  • 132
    • 0020458747 scopus 로고
    • Two-step methods for the numerical solution of the Schrödinger equation
    • Raptis A. D.: Two-step methods for the numerical solution of the Schrödinger equation. Computing 28, 373-378 (1982).
    • (1982) Computing , vol.28 , pp. 373-378
    • Raptis, A.D.1
  • 133
    • 0343622378 scopus 로고
    • Two-step almost P-stable complete in phase methods for the numerical integration of second order periodic initial-value problems
    • Simos T. E.: Two-step almost P-stable complete in phase methods for the numerical integration of second order periodic initial-value problems. Int. J. Comput. Math. 46, 77-85 (1992).
    • (1992) Int. J. Comput. Math. , vol.46 , pp. 77-85
    • Simos, T.E.1
  • 134
    • 2442647571 scopus 로고    scopus 로고
    • Dissipative trigonometrically-fitted methods for linear second-order IVPs with oscillating solution
    • Simos T. E.: Dissipative trigonometrically-fitted methods for linear second-order IVPs with oscillating solution. Appl. Math. Lett. 17(5), 601-607 (2004).
    • (2004) Appl. Math. Lett. , vol.17 , Issue.5 , pp. 601-607
    • Simos, T.E.1
  • 135
    • 31244436593 scopus 로고    scopus 로고
    • Exponentially-fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions
    • Simos T. E.: Exponentially-fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions. Appl. Math. Lett. 15(2), 217-225 (2002).
    • (2002) Appl. Math. Lett. , vol.15 , Issue.2 , pp. 217-225
    • Simos, T.E.1
  • 136
    • 0013397128 scopus 로고    scopus 로고
    • A modified Runge-Kutta method for the numerical solution of ODE's with oscillation solutions
    • Simos T. E.: A modified Runge-Kutta method for the numerical solution of ODE's with oscillation solutions. Appl. Math. Lett. 9(6), 61-66 (1996).
    • (1996) Appl. Math. Lett. , vol.9 , Issue.6 , pp. 61-66
    • Simos, T.E.1
  • 137
    • 43949167153 scopus 로고
    • A high-order predictor-corrector method for periodic IVPS
    • Simos T. E.: A high-order predictor-corrector method for periodic IVPS. Appl. Math. Lett. 6(5), 9-12 (1993).
    • (1993) Appl. Math. Lett. , vol.6 , Issue.5 , pp. 9-12
    • Simos, T.E.1
  • 138
    • 38249003377 scopus 로고
    • A new variable-step method for the numerical-integration of special 2nd-order initial-value problems and their application to the one-dimensional Schrödinger-equation
    • Simos T. E.: A new variable-step method for the numerical-integration of special 2nd-order initial-value problems and their application to the one-dimensional Schrödinger-equation. Appl. Math. Lett. 6(3), 67-73 (1993).
    • (1993) Appl. Math. Lett. , vol.6 , Issue.3 , pp. 67-73
    • Simos, T.E.1
  • 139
    • 84897576381 scopus 로고    scopus 로고
    • Exponentially and trigonometrically fitted methods for the solution of the Schrd̈inger equation
    • (in press)
    • T. E. Simos, Exponentially and trigonometrically fitted methods for the solution of the Schrd̈inger equation. Acta. Appl. Math. (2009) (in press).
    • (2009) Acta. Appl. Math.
    • Simos, T.E.1
  • 140
    • 67650001624 scopus 로고    scopus 로고
    • Optimization as a function of the phase-lag order of nonlinear explicit two-step P-stable method for linear periodic IVPs
    • Stavroyiannis S., Simos T. E.: Optimization as a function of the phase-lag order of nonlinear explicit two-step P-stable method for linear periodic IVPs. Appl. Numer. Math. 59(10), 2467-2474 (2009).
    • (2009) Appl. Numer. Math. , vol.59 , Issue.10 , pp. 2467-2474
    • Stavroyiannis, S.1    Simos, T.E.2
  • 141
    • 0039754348 scopus 로고
    • A numerov-type method for the numerical-solution of the radial Schrödinger-equation
    • Simos T. E.: A numerov-type method for the numerical-solution of the radial Schrödinger-equation. Appl. Numer. Math. 7(2), 201-206 (1991).
    • (1991) Appl. Numer. Math. , vol.7 , Issue.2 , pp. 201-206
    • Simos, T.E.1
  • 142
    • 0035541118 scopus 로고    scopus 로고
    • A fourth algebraic order exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation
    • Simos T. E.: A fourth algebraic order exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation. Ima J. Numer. Anal. 21(4), 919-931 (2001).
    • (2001) Ima J. Numer. Anal. , vol.21 , Issue.4 , pp. 919-931
    • Simos, T.E.1
  • 143
    • 30244570721 scopus 로고
    • Some new 4-step exponential-fitting methods for the numerical-solution of the radial SchrÖdinger-equation
    • Simos T. E.: Some new 4-step exponential-fitting methods for the numerical-solution of the radial SchrÖdinger-equation. Ima J. Numer. Anal. 11(3), 347-356 (1991).
    • (1991) Ima J. Numer. Anal. , vol.11 , Issue.3 , pp. 347-356
    • Simos, T.E.1
  • 144
    • 0005354881 scopus 로고
    • An explicit high-order predictor-corrector method for periodic initial-value problems
    • Simos T. E.: An explicit high-order predictor-corrector method for periodic initial-value problems. Math. Model. Method. Appl. Sci. 5(2), 159-166 (1995).
    • (1995) Math. Model. Method. Appl. Sci. , vol.5 , Issue.2 , pp. 159-166
    • Simos, T.E.1
  • 145
    • 0347724134 scopus 로고    scopus 로고
    • Zero dissipative, explicit Numerov-type methods for second order IVPs with oscillating solutions
    • Simos TE T. E., Famelis I. T., Tsitouras C.: Zero dissipative, explicit Numerov-type methods for second order IVPs with oscillating solutions. Numer. Algorithm. 34(1), 27-40 (2003).
    • (2003) Numer. Algorithm. , vol.34 , Issue.1 , pp. 27-40
    • Simos Te, T.E.1    Famelis, I.T.2    Tsitouras, C.3
  • 146
    • 77958409581 scopus 로고
    • Symmetric multistep methods for periodic initial values problems
    • Lambert J. D., Watson I. A.: Symmetric multistep methods for periodic initial values problems. J. Inst. Math. Appl. 18, 189-202 (1976).
    • (1976) J. Inst. Math. Appl. , vol.18 , pp. 189-202
    • Lambert, J.D.1    Watson, I.A.2
  • 147
    • 0000926830 scopus 로고
    • A four-step phase-fitted method for the numerical integration of second order initial-value problem
    • Raptis A. D., Simos T. E.: A four-step phase-fitted method for the numerical integration of second order initial-value problem. BIT 31, 160-168 (1991).
    • (1991) Bit , vol.31 , pp. 160-168
    • Raptis, A.D.1    Simos, T.E.2
  • 149
    • 0020983418 scopus 로고
    • Uncoditionally stable Noumerov-type methods for second order differential equations
    • Chawla M. M.: Uncoditionally stable Noumerov-type methods for second order differential equations. BIT 23, 541-542 (1983).
    • (1983) Bit , vol.23 , pp. 541-542
    • Chawla, M.M.1
  • 150
    • 0021578695 scopus 로고
    • A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
    • Chawla M. M., Rao P. S.: A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. J. Comput. Appl. Math. 11(3), 277-281 (1984).
    • (1984) J. Comput. Appl. Math. , vol.11 , Issue.3 , pp. 277-281
    • Chawla, M.M.1    Rao, P.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.