Computation of the eigenvalues of the Schrödinger equation by exponentially-fitted Runge-Kutta-Nyström methods

Computer Physics Communications

Volumn 180, Issue 2, 2009, Pages 167-176

  Kalogiratou, Z ^a   Monovasilis, Th ^a   Simos, T E ^b  

^a UNIVERSITY OF WESTERN MACEDONIA   (Greece)

^b UNIVERSITY OF PELOPONNESE   (Greece)

Author keywords

Runge Kutta Nystr m methods; Schr dinger equation; Trigonometrically fitted

Indexed keywords

OSCILLATORS (ELECTRONIC); OSCILLATORS (MECHANICAL);

ANHARMONIC OSCILLATORS; DIFFERENTIAL SYSTEMS; EIGENVALUES; HARMONIC OSCILLATORS; LINEAR COMBINATIONS; TRIGONOMETRICALLY FITTED;

RUNGE KUTTA METHODS;

EID: 58249087012     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2008.09.001     Document Type: Article

References (20)

1. Dormand J.R., El-Mikkawy M.E., and Prince P.J. Families of Runge-Kutta-Nyström formulae. IMA Journal of Numerical Analysis 7 (1987) 235-250
2. Franco J.M. Exponentially fitted explicit Runge-Kutta-Nyström methods. Journal of Computational and Applied Mathematics 167 (2004) 1-19
3. Hairer E., Norsett S., and Wanner G. Solving Ordinary Differential Equations I: Nonstiff Problems (2002), Springer-Verlag
4. Ixaru L.Gr., and Vanden Berghe G. Exponential Fitting (2004), Kluwer Academic Publishers
5. Monovasilis Th., Kalogiratou Z., and Simos T.E. Exponentially fitted symplectic methods for the Schrödinger equation. Journal of Mathematical Chemistry 37 (2005) 263-270
6. Simos T.E. An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions. Computer Physics Communications 115 (1998) 1-8
7. Simos T.E. Exponentially fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions. Applied Mathematics Letters 15 (2002) 217-225
8. Simos T.E. Exponentially fitted Runge-Kutta methods for the numerical solution of the Schrödinger equation and related problems. Computational Materials Science 18 (2000) 315-332
9. Vanden Berghe G., De Meyer H., Van Daele M., and Van Hecke T. Exponentially fitted Runge-Kutta-Nyström methods. Computer Physics Communications 123 (1999) 7-15
10. Vanden Berghe G., De Meyer H., Van Daele M., and Van Hecke T. Exponentially fitted Runge-Kutta methods. Journal of Computational and Applied Mathematics 125 (2000) 107-115
11. Van de Vyver H. A symplectic exponentially fitted modified Runge-Kutta-Nyström method for the numerical integration of orbital problems, New Astronomy 10 (2005) 261-269
12. Van de Vyver H. Modified explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation. Applied Mathematics and Computation 171 (2005) 1025-1036
13. Cash J.R., and Girdlestone S. Variable step Runge-Kutta-Nyström methods for the numerical solution of reversible systems. J. Numer. Anal. Indust. Appl. Math. (JNAIAM) 1 1 (2006) 59-80
14. Vanden Berghe G., and Van Daele M. Exponentially-fitted Störmer/Verlet methods. J. Numer. Anal. Indust. Appl. Math. (JNAIAM) 1 3 (2006) 241-255
15. Capper S.D., Cash J.R., and Moore D.R. Lobatto-Obrechkoff formulae for 2nd order two-point boundary value problems. J. Numer. Anal. Indust. Appl. Math. (JNAIAM) 1 1 (2006) 13-25
16. Aceto L., Pandolfi R., and Trigiante D. Stability analysis of linear multistep methods via polynomial type variation. J. Numer. Anal. Indust. Appl. Math. (JNAIAM) 2 1-2 (2007) 1-9
17. Dewar M. Embedding a general-purpose numerical library in an interactive environment. J. Numer. Anal. Indust. Appl. Math. (JNAIAM) 3 1-2 (2008) 17-26
18. Kierzenka J., and Shampine L.F. A BVP solver that controls residual and error. J. Numer. Anal. Indust. Appl. Math. (JNAIAM) 3 1-2 (2008) 27-41
19. Knapp R. A method of lines framework in Mathematica. J. Numer. Anal. Indust. Appl. Math. (JNAIAM) 3 1-2 (2008) 43-59
20. Sofroniou M., and Spaletta G. Extrapolation methods in Mathematica. J. Numer. Anal. Indust. Appl. Math. (JNAIAM) 3 1-2 (2008) 105-121