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Volumn 29, Issue 3, 2001, Pages 177-189

A family of P-stable eighth algebraic order methods with exponential fitting facilities

Author keywords

Error control; P stability; Phase shift problem; Scattering problems; Schr dinger equation; Variable step

Indexed keywords


EID: 0035315407     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1010972322815     Document Type: Article
Times cited : (45)

References (31)
  • 1
    • 0034276333 scopus 로고    scopus 로고
    • A P-stable hybrid exponentially-fitted method for the numerical integration of the Schrödinger equiation
    • T.E. Simos and P.S. Williams, A P-stable hybrid exponentially-fitted method for the numerical integration of the Schrödinger equiation, Comput. Phys. Comm. 131 (2000) 109-119.
    • (2000) Comput. Phys. Comm. , vol.131 , pp. 109-119
    • Simos, T.E.1    Williams, P.S.2
  • 2
    • 0001237676 scopus 로고    scopus 로고
    • On finite difference methods for the solution of the Schrödinger equation
    • T.E. Simos and P.S. Williams, On finite difference methods for the solution of the Schrödinger equation, Comput. Chem. 23 (1999) 513-554.
    • (1999) Comput. Chem. , vol.23 , pp. 513-554
    • Simos, T.E.1    Williams, P.S.2
  • 3
    • 0002207932 scopus 로고    scopus 로고
    • Embedded methods for the numerical solution of the Schrödinger equation
    • G. Avdelas and T.E. Simos, Embedded methods for the numerical solution of the Schrödinger equation, Comput. Math. Appl. 31 (1996) 85-102.
    • (1996) Comput. Math. Appl. , vol.31 , pp. 85-102
    • Avdelas, G.1    Simos, T.E.2
  • 4
    • 0031326292 scopus 로고    scopus 로고
    • Eighth order methods with minimal phase-lag for accurate computations for the elastic scattering phase-shift problem
    • T.E. Simos, Eighth order methods with minimal phase-lag for accurate computations for the elastic scattering phase-shift problem, J. Math. Chem. 21 (1997) 359-372.
    • (1997) J. Math. Chem. , vol.21 , pp. 359-372
    • Simos, T.E.1
  • 5
    • 0039065106 scopus 로고    scopus 로고
    • Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations
    • T.E. Simos, Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations, J. Math. Chem. 24 (1998) 23-37.
    • (1998) J. Math. Chem. , vol.24 , pp. 23-37
    • Simos, T.E.1
  • 6
    • 0033429763 scopus 로고    scopus 로고
    • A family of P-stable exponentially-fitted methods for the numerical solution of the Schrödinger equation
    • T.E. Simos, A family of P-stable exponentially-fitted methods for the numerical solution of the Schrödinger equation, J. Math. Chem. 25 (1999) 65-84.
    • (1999) J. Math. Chem. , vol.25 , pp. 65-84
    • Simos, T.E.1
  • 7
    • 0033114512 scopus 로고    scopus 로고
    • Embedded eighth order methods for the numerical solution of the Schrödinger equation
    • G. Avdelas and T.E. Simos, Embedded eighth order methods for the numerical solution of the Schrödinger equation, J. Math. Chem. 25 (1999) 327-341.
    • (1999) J. Math. Chem. , vol.25 , pp. 327-341
    • Avdelas, G.1    Simos, T.E.2
  • 8
    • 0007190029 scopus 로고    scopus 로고
    • High order Bessel fitting methods for the numerical integration of the Schrödinger equation
    • in press
    • J. Vigo-Aguiar, High order Bessel fitting methods for the numerical integration of the Schrödinger equation, Comput. Chem. (2000), in press.
    • (2000) Comput. Chem.
    • Vigo-Aguiar, J.1
  • 9
    • 0347357926 scopus 로고    scopus 로고
    • A general procedure to construct adapted methods to oscillatory problems
    • J. Vigo-Aguiar and J.M. Ferrandiz, A general procedure to construct adapted methods to oscillatory problems, SIAM J. Numer. Anal. 35 (1998) 1684-1719.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 1684-1719
    • Vigo-Aguiar, J.1    Ferrandiz, J.M.2
  • 11
    • 0003250244 scopus 로고    scopus 로고
    • New methods in computational quantum mechanics
    • Wiley, New York
    • I. Prigogine and S. Rice (eds.), New Methods in Computational Quantum Mechanics, Advances in Chemical Physics, Vol. 93 (Wiley, New York, 1997).
    • (1997) Advances in Chemical Physics , vol.93
    • Prigogine, I.1    Rice, S.2
  • 12
    • 0001248061 scopus 로고
    • (Extended) Numerov method for computing eigenvalues of specific Schrödinger equations
    • V. Fack and G. Vanden Berghe, (Extended) Numerov method for computing eigenvalues of specific Schrödinger equations, J. Phys. A: Math. Gen. 20 (1987) 4153.
    • (1987) J. Phys. A: Math. Gen. , vol.20 , pp. 4153
    • Fack, V.1    Berghe, G.V.2
  • 13
    • 36149040101 scopus 로고
    • A finite difference approach for the calculation of perturbed oscillator energies
    • V. Fack and G. Vanden Berghe, A finite difference approach for the calculation of perturbed oscillator energies, J. Phys. A: Math. Gen. 18 (1987) 3355.
    • (1987) J. Phys. A: Math. Gen. , vol.18 , pp. 3355
    • Fack, V.1    Berghe, G.V.2
  • 14
    • 0021505273 scopus 로고
    • A high order method for the numerical solution of the one-dimensional Schrödinger equation
    • J.R. Cash and A.D. Raptis, A high order method for the numerical solution of the one-dimensional Schrödinger equation, Comput. Phys. Comm. 33 (1984) 299-304.
    • (1984) Comput. Phys. Comm. , vol.33 , pp. 299-304
    • Cash, J.R.1    Raptis, A.D.2
  • 15
    • 0001330331 scopus 로고
    • Numerical methods for y″ = f (x, y) via rational approximation for the cosine
    • J.P. Coleman, Numerical methods for y″ = f (x, y) via rational approximation for the cosine, IMA J. Numer. Anal. 9 (1989) 145-165.
    • (1989) IMA J. Numer. Anal. , vol.9 , pp. 145-165
    • Coleman, J.P.1
  • 16
    • 77958409581 scopus 로고
    • Symmetric multistep methods for periodic initial value problems
    • J.D. Lambert and I.A. Watson, Symmetric multistep methods for periodic initial value problems, J. Inst. Math. Appl. 18 (1976) 189-202.
    • (1976) J. Inst. Math. Appl. , vol.18 , pp. 189-202
    • Lambert, J.D.1    Watson, I.A.2
  • 17
    • 0021316047 scopus 로고
    • Phase properties of high order almost P-stable formulae
    • R.M. Thomas, Phase properties of high order almost P-stable formulae, BIT 24 (1984) 225-238.
    • (1984) BIT , vol.24 , pp. 225-238
    • Thomas, R.M.1
  • 18
    • 0023366337 scopus 로고
    • Explicit Runge-Kutta (-Nyström) methods with reduced phase errors for computing oscillating solutions
    • P.J. van der Houwen and B.P. Sommeijer, Explicit Runge-Kutta (-Nyström) methods with reduced phase errors for computing oscillating solutions, SIAM J. Numer. Anal. 24 (1987) 595-617.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 595-617
    • Van Der Houwen, P.J.1    Sommeijer, B.P.2
  • 19
    • 0001067740 scopus 로고
    • A two-step method for the numerical solution of the radial Schrödinger equation
    • T.E. Simos and G. Mousadis, A two-step method for the numerical solution of the radial Schrödinger equation, Comput. Math. Appl. 29 (1995) 31-37.
    • (1995) Comput. Math. Appl. , vol.29 , pp. 31-37
    • Simos, T.E.1    Mousadis, G.2
  • 20
    • 0016971912 scopus 로고
    • Solving nonstiff ordinary differential equations - The state of the art
    • L.F. Shampine, H.A. Watts and S.M. Davenport, Solving nonstiff ordinary differential equations - the state of the art, SIAM Rev. 18 (1976) 376-411.
    • (1976) SIAM Rev. , vol.18 , pp. 376-411
    • Shampine, L.F.1    Watts, H.A.2    Davenport, S.M.3
  • 21
    • 0001401038 scopus 로고
    • The numerical solution of coupled differential equations arising from the Schrödinger equation
    • A.C. Allison, The numerical solution of coupled differential equations arising from the Schrödinger equation, J. Comput. Phys. 6 (1970) 378-391.
    • (1970) J. Comput. Phys. , vol.6 , pp. 378-391
    • Allison, A.C.1
  • 23
    • 0000633647 scopus 로고
    • Quantum mechanical (phase shift) analysis of differential elastic scattering of molecular beams
    • R.B. Berstein, Quantum mechanical (phase shift) analysis of differential elastic scattering of molecular beams, J. Chem. Phys. 33 (1960) 795-804.
    • (1960) J. Chem. Phys. , vol.33 , pp. 795-804
    • Berstein, R.B.1
  • 24
    • 0001752844 scopus 로고
    • A variable step method for the numerical integration of the one-dimensional Schrödinger equation
    • A.D. Raptis and J.R. Cash, A variable step method for the numerical integration of the one-dimensional Schrödinger equation, Comput. Phys. Comm. 36 (1985) 113-119.
    • (1985) Comput. Phys. Comm. , vol.36 , pp. 113-119
    • Raptis, A.D.1    Cash, J.R.2
  • 25
    • 0030367389 scopus 로고    scopus 로고
    • An eighth order method with minimal phase-lag for accurate computations for the elastic scattering phase-shift problem
    • T.E. Simos, An eighth order method with minimal phase-lag for accurate computations for the elastic scattering phase-shift problem, Internat. J. Modern Phys. C 7 (1996) 825-835.
    • (1996) Internat. J. Modern Phys. C , vol.7 , pp. 825-835
    • Simos, T.E.1
  • 26
    • 0000410643 scopus 로고    scopus 로고
    • Computer algebra programmes for the construction of a family of Numerov-type exponentially-fitted methods for the numerical solution of the Schrödinger equation
    • T.E. Simos and P.S. Williams, Computer algebra programmes for the construction of a family of Numerov-type exponentially-fitted methods for the numerical solution of the Schrödinger equation, Comput. Chem. 22 (1998) 185-218.
    • (1998) Comput. Chem. , vol.22 , pp. 185-218
    • Simos, T.E.1    Williams, P.S.2
  • 27
    • 0000647840 scopus 로고    scopus 로고
    • An explicit eighth order method with minimal phase-lag for accurate computations of eigenvalues, resonances and phase shifts
    • T.E. Simos and G. Tougelidis, An explicit eighth order method with minimal phase-lag for accurate computations of eigenvalues, resonances and phase shifts, Comput. Chem. 21 (1997) 327-334.
    • (1997) Comput. Chem. , vol.21 , pp. 327-334
    • Simos, T.E.1    Tougelidis, G.2
  • 28
    • 0001590149 scopus 로고    scopus 로고
    • Bessel and Neuman-fitted methods for the numerical solution of the radial Schrödinger equation
    • T.E. Simos and P.S. Williams, Bessel and Neuman-fitted methods for the numerical solution of the radial Schrödinger equation, Comput. Chem. 21 (1997) 175-179.
    • (1997) Comput. Chem. , vol.21 , pp. 175-179
    • Simos, T.E.1    Williams, P.S.2
  • 31
    • 0000625927 scopus 로고    scopus 로고
    • New P-stable high-order methods with minimal phase-lag for the numerical integration of the radial Schrödinger equation
    • T.E. Simos, New P-stable high-order methods with minimal phase-lag for the numerical integration of the radial Schrödinger equation, Phys. Scripta 55 (1997) 644-650.
    • (1997) Phys. Scripta , vol.55 , pp. 644-650
    • Simos, T.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.