메뉴 건너뛰기




Volumn 7, Issue 2, 2013, Pages 433-437

A modified runge-kutta-nyström method by using phase lag properties for the numerical solution of orbital problems

Author keywords

Derivatives; Initial value problems; Orbital problems; Oscillating solution; Phase fitted'8Amplification fitted; Runge kutta nystr m methods

Indexed keywords


EID: 84873473669     PISSN: 19350090     EISSN: None     Source Type: Journal    
DOI: 10.12785/amis/070202     Document Type: Article
Times cited : (152)

References (28)
  • 1
    • 0023366337 scopus 로고
    • Explicit Runge-Kutta-Nyström methods with reduced phase errors for computing oscillating solutions
    • P.J. van der Houwen, 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
  • 3
    • 0034744534 scopus 로고    scopus 로고
    • A modified Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation and related problems
    • T. E. Simos, Jesu's Vigo Aguiar, A modified Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation and related problems, Comput. Chem. 25 (2001) 275-281.
    • (2001) Comput. Chem. , vol.25 , pp. 275-281
    • Simos, T.E.1    Aguiar, J.V.2
  • 4
    • 70349509116 scopus 로고    scopus 로고
    • A new Numerov-type method for the numerical solution of the Schrödinger equation
    • T. E. Simos, A new Numerov-type method for the numerical solution of the Schrödinger equation, J. Math. Chem. 46 (2009) 9811007.
    • (2009) J. Math. Chem. , vol.46 , pp. 9811007
    • Simos, T.E.1
  • 5
    • 77955774009 scopus 로고    scopus 로고
    • A modified phase-fitted and amplification-fitted Runge-Kutta-Nyström method for the numerical solution of the radial Schröinger equation
    • D.F. Papadopoulos, Z.A. Anastassi, T.E. Simos, A modified phase-fitted and amplification-fitted Runge-Kutta-Nyström method for the numerical solution of the radial Schröinger equation, J. Mol. Model., 16 (2010) 1339-1346.
    • (2010) J. Mol. Model. , vol.16 , pp. 1339-1346
    • Papadopoulos, D.F.1    Anastassi, Z.A.2    Simos, T.E.3
  • 6
    • 79960758578 scopus 로고    scopus 로고
    • A New Methodology for the Construction of Optimized Runge-Kutta-Nyström Methods
    • D.F. Papadopoulos, T.E. Simos, A New Methodology for the Construction of Optimized Runge-Kutta-Nyström Methods, J. of Modern Physics C, 22 (2011) 623-634.
    • (2011) J. of Modern Physics C , vol.22 , pp. 623-634
    • Papadopoulos, D.F.1    Simos, T.E.2
  • 7
    • 77957352499 scopus 로고    scopus 로고
    • High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation
    • Ibraheem Alolyan and T.E. Simos, High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation , J. Math. Chem. 48 (2010) 925-958.
    • (2010) J. Math. Chem. , vol.48 , pp. 925-958
    • Alolyan, I.1    Simos, T.E.2
  • 8
    • 80052265429 scopus 로고    scopus 로고
    • A family of ten-step methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation
    • Ibraheem Alolyan and T.E. Simos, A family of ten-step methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation, J. Math. Chem. 49 (2011) 1843-1888.
    • (2011) J. Math. Chem. , vol.49 , pp. 1843-1888
    • Alolyan, I.1    Simos, T.E.2
  • 9
    • 79960304267 scopus 로고    scopus 로고
    • A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation
    • Konguetsof A, A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation, J. Math. Chem. 49 (2011) 1330-1356.
    • (2011) J. Math. Chem. , vol.49 , pp. 1330-1356
    • Konguetsof, A.1
  • 10
    • 72949109296 scopus 로고    scopus 로고
    • An optimized explicit Runge-Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problems
    • A. A. Kosti, Z. A. Anastassi and T. E. Simos, An optimized explicit Runge-Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problems, J. Math. Chem. 47 (2010) 315-330.
    • (2010) J. Math. Chem. , vol.47 , pp. 315-330
    • Kosti, A.A.1    Anastassi, Z.A.2    Simos, T.E.3
  • 12
    • 33645269140 scopus 로고
    • Stabilization of Cowell's method
    • E. Stiefel and D. G. Bettis, Stabilization of Cowell's method, Numerische Mathematik, 13(2) (1969) 154-175
    • (1969) Numerische Mathematik , vol.13 , Issue.2 , pp. 154-175
    • Stiefel, E.1    Bettis, D.G.2
  • 13
    • 0042785945 scopus 로고    scopus 로고
    • A generator of hybrid symmetric four-step methods for the numerical solution of the Schrödinger equation
    • A. Konguetsof and T.E. Simos, A generator of hybrid symmetric four-step methods for the numerical solution of the Schrödinger equation, Journal of Computational and Applied Mathematics 158(1) 93-106(2003)
    • (2003) Journal of Computational and Applied Mathematics , vol.158 , Issue.1 , pp. 93-106
    • Konguetsof, A.1    Simos, T.E.2
  • 16
    • 0043287096 scopus 로고    scopus 로고
    • Trigonometrically fitted predictor-corrector methods for IVPs with oscillating solutions
    • G. Psihoyios and T.E. Simos, Trigonometrically fitted predictor-corrector methods for IVPs with oscillating solutions, Journal of Computational and Applied Mathematics 158(1) 135-144(2003)
    • (2003) Journal of Computational and Applied Mathematics , vol.158 , Issue.1 , pp. 135-144
    • Psihoyios, G.1    Simos, T.E.2
  • 17
    • 0347724134 scopus 로고    scopus 로고
    • Zero dissipative, explicit Numerov-type methods for second order IVPs with oscillating solutions
    • T.E. Simos, I.T. Famelis and C. Tsitouras, Zero dissipative, explicit Numerov-type methods for second order IVPs with oscillating solutions, Num. Algor. 34(1) 27-40(2003)
    • (2003) Num. Algor. , vol.34 , Issue.1 , pp. 27-40
    • Simos, T.E.1    Famelis, I.T.2    Tsitouras, C.3
  • 18
    • 3242667053 scopus 로고    scopus 로고
    • Dissipative trigonometrically-fitted methods for linear second-order IVPs with oscillating solution
    • T.E. Simos, 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
  • 19
    • 11044225131 scopus 로고    scopus 로고
    • Runge-Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics
    • K. Tselios and T.E. Simos, Runge-Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics, Journal of Computational and Applied Mathematics Volume: 175(1) 173-181(2005)
    • (2005) Journal of Computational and Applied Mathematics Volume , vol.175 , Issue.1 , pp. 173-181
    • Tselios, K.1    Simos, T.E.2
  • 20
    • 11044223038 scopus 로고    scopus 로고
    • Multiderivative methods of eighth algrebraic order with minimal phase-lag for the numerical solution of the radial Schrödinger equation
    • D.P. Sakas and T.E. Simos, Multiderivative methods of eighth algrebraic order with minimal phase-lag for the numerical solution of the radial Schrödinger equation, Journal of Computational and Applied Mathematics 175(1) 161-172(2005)
    • (2005) Journal of Computational and Applied Mathematics , vol.175 , Issue.1 , pp. 161-172
    • Sakas, D.P.1    Simos, T.E.2
  • 21
    • 11044230652 scopus 로고    scopus 로고
    • A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions
    • G. Psihoyios and T.E. Simos, A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions, Journal of Computational and Applied Mathematics 175(1) 137-147(2005)
    • (2005) Journal of Computational and Applied Mathematics , vol.175 , Issue.1 , pp. 137-147
    • Psihoyios, G.1    Simos, T.E.2
  • 23
    • 68449089413 scopus 로고    scopus 로고
    • Closed Newton-Cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problems
    • T.E. Simos, Closed Newton-Cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problems, Appl. Math. Lett. 22 (10) 1616-1621(2009)
    • (2009) Appl. Math. Lett. , vol.22 , Issue.10 , pp. 1616-1621
    • Simos, T.E.1
  • 24
    • 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
    • S. Stavroyiannis and T.E. Simos, Optimization as a function of the phase-lag order of nonlinear explicit two-step P-stable method for linear periodic IVPs, Appl. Num. Math. 59(10) 2467-2474(2009)
    • (2009) Appl. Num. Math. , vol.59 , Issue.10 , pp. 2467-2474
    • Stavroyiannis, S.1    Simos, T.E.2
  • 25
    • 77957331657 scopus 로고    scopus 로고
    • Exponentially and Trigonometrically Fitted Methods for the Solution of the Schrödinger Equation
    • T.E. Simos, Exponentially and Trigonometrically Fitted Methods for the Solution of the Schrödinger Equation, Acta Appl. Math. 110(3) 1331-1352(2010)
    • (2010) Acta Appl. Math. , vol.110 , Issue.3 , pp. 1331-1352
    • Simos, T.E.1
  • 26
    • 84862274750 scopus 로고    scopus 로고
    • New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time Integration
    • Article ID 182536, 15 pages, 2012 doi:10.1155/2012/182536
    • T. E. Simos, New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time Integration, Abstract and Applied Analysis, Volume 2012, Article ID 182536, 15 pages, 2012 doi:10.1155/2012/182536
    • (2012) Abstract and Applied Analysis
    • Simos, T.E.1
  • 27
    • 84861088351 scopus 로고    scopus 로고
    • Optimizing a Hybrid Two-Step Method for the Numerical Solution of the Schrödinger Equation and Related Problems with Respect to Phase-Lag
    • Article ID 420387, 17 pages, doi:10.1155/2012/420387, 2012
    • T.E. Simos, Optimizing a Hybrid Two-Step Method for the Numerical Solution of the Schrödinger Equation and Related Problems with Respect to Phase-Lag, Journal of Applied Mathematics, Volume 2012, Article ID 420387, 17 pages, doi:10.1155/2012/420387, 2012
    • (2012) Journal of Applied Mathematics
    • Simos, T.E.1
  • 28
    • 84861723014 scopus 로고    scopus 로고
    • A parametric symmetric linear four-step method for the efficient integration of the Schrödinger equation and related oscillatory problems
    • Z.A. Anastassi and T.E. Simos, A parametric symmetric linear four-step method for the efficient integration of the Schrödinger equation and related oscillatory problems, Journal of Computational and Applied Mathematics 236 38803889(2012)
    • (2012) Journal of Computational and Applied Mathematics , vol.236 , pp. 3880-3889
    • Anastassi, Z.A.1    Simos, T.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.