New Embedded Explicit Methods with Minimal Phase-lag for the Numerical Integration of the Schrödinger Equation

Computers and Chemistry

Volumn 22, Issue 5, 1998, Pages 433-440

  Simos, T E ^a,b  

^a DEMOCRITUS UNIVERSITY OF THRACE   (Greece)

^b NONE   (Greece)

Author keywords

Coupled differential equations; Embedded methods; Explicit methods; Finite difference methods; Multistep methods; Phase lag; Schr dinger equations

Indexed keywords

EID: 0001190986     PISSN: 00978485     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0097-8485(98)00003-5     Document Type: Article

References (33)

1. Allison, A. C. (1970) Journal of Computational Physics 6, 378.
2. Arthurs, A. M. and Dalgarno, A. (1060) Proceedings of the Royal Society A 256, 540.
3. Baylis, W. E. and Peel, S. J. (1982) Computers and Physics Communications 25, 7.
4. Bernstein, R. B. (1960) Journal of Chemical Physics 33, 795.
5. Bernstein, R. B., Dalgarno, A., Massey, H. and Percival, I. C. (1963) Proceedings of the Royal Society of Series A 274, 427.
6. Brusa, L. and Nigro, L. (1980) International Journal of Numerical Methods in Engineering 15, 685.
7. Cash, J. R. and Raptis, A. D. (1984) Computers and Physics Communications 33, 299.
8. Cash, J. R. and Raptis, A. D. (1985) Computers and Physics Communications 36, 113.
9. Chawla, M. M. and Rao, P. S. (1986) Journal of Computers and Applied Mathematics 15, 329.
10. Chawla, M. M., Rao, P. S. and Neta, B. (1987) Journal of Computers and Applied Mathematics 16, 365.
11. Chawla, M. M. and Rao, P. S. (1986) Journal of Computers and Applied Mathematics 16, 233.
12. Coleman, J. P. (1989) IMA Journal of Numerical Analysis 9, 145.
13. Dormand, J. R. and Prince, P. J. (1987) Computers and Mathematical Applications 13, 937.
14. Dormand, J. R., El-Mikkawy, M. E. A. and Prince, P. J. (1987) IMA Journal of Numerical Analysis 7, 423.
15. Hairer, E., Norsett, S. P. and Wanner, G. (1987) Solving Ordinary Differential Equations I. Springer, Berlin.
16. Hajj, F. Y., Kobeissi, H. and Nassif, N. (1974) Journal of Computational Physics 16, 150.
17. van der Houwen, P. J. and Sommeijer, B. P. (1987) SIAM Journal of Numerical Analysis 24, 595.
18. Killingbeck, J. (1987) Journal of Physics A: Math. Gen. 20, 1411.
19. Kobeissi, H. and Kobeissi, M. (1988a) Journal of Computers and Chemistry 9, 844.
20. Kobeissi, H. and Kobeissi, M. (1988b) Journal of Computers and Physics 77, 501.
21. Kobeissi, H., Kobeissi, M. and El-Hajj, Ali (1989) Journal of Physics A: Math. Gen. 22, 287.
22. Kroes, G. J. (1992) Computers and Physics Communications 70, 41.
23. Landau, L. D. and Lifshitz, F. M. (1965) Quantum Mechanics. Pergamon, New York.
24. Raptis, A. D. and Simos, T. E. (1991) BIT 31, 160.
25. Simos, T. E. (1990) Numerical solution of ordinary differential equations with periodical solution. Ph.D. thesis. National Technical University of Athens, Greece.
26. Simos, T. E. (1991) International Journal of Computational Mathematics 39, 135.
27. Simos, T. E. (1992) Applied Mathematics and Computers 49, 261.
28. Simos, T. E. (1995) Mathematical Modelling and Mathematical Applied Science 5, 159.
29. Simos, T. E. (1996) International Journal of Modernized Physics C 7, 33.
30. Simos, T. E. (1997) Computational Chemistry 21, 125.
31. Simos, T. E. and Raptis, A. D. (1990) Computing 45, 175.
32. Simos, T. E. and Williams, P. S. (1997) Computational Chemistry 21, 175.
33. Vanden, Berghe G., Fack, V. and De Meyer, H. E. (1989) Journal of Computers and Applied Mathematics 29, 391.