Computer Algebra Programmes for the Construction of a Family of Numerov-type Exponentially-fitted Methods for the Numerical Solution of the Schrödinger Equation

Computers and Chemistry

Volumn 22, Issue 2-3, 1998, Pages 185-218

  Simos, T E ^a   Williams, P S ^b  

^a DEMOCRITUS UNIVERSITY OF THRACE   (Greece)

^b LONDON METROPOLITAN UNIVERSITY   (United Kingdom)

Author keywords

Coupled equations; Exponentially fitted methods; Numerov type methods; Phase shift problem; Predictor corrector methods; Schr dinger equation

Indexed keywords

EID: 0000410643     PISSN: 00978485     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0097-8485(97)00051-X     Document Type: Article

References (37)

1. Allison, A. C. (1970) J. Comput. Phys. 6, 378.
2. Arthurs, A. M. and Dalgarno, A. (1960) Proceedings of the Royal Society, Series A 256, 540.
3. Bernstein, R. B. (1960) Journal of Chemical Physics 33, 795.
4. Bernstein, R. B., Dalgarno, A., Massey, H. and Percival, I. C. (1963) Proceedings of the Royal Society, Series A 274, 427.
5. Blatt, J. M. (1967) J. Comput. Phys. 1, 382.
6. Cash, J. R. and Raptis, A. D. (1984) Comput. Phys. Commun. 33, 299.
7. Cash, J. R., Raptis, A. D. and Simos, T. E. (1990) J. Comput. Phys. 91, 413.
8. Coleman, J. P. (1989) IMA J. Numer. Anal. 9, 145.
9. Cooley, J. W. (1961) Math. Comp. 15, 363.
10. Hairer, E., Nørsett, S. P. and Wanner, G. (1987) Solving Ordinary Differential Equations I. Springer-Verlag, Berlin.
11. Hajj, F. Y., Kobeissi, H. and Nassif, N. R. (1974) J. Comput. Phys. 16, 150.
12. Henrici, P. (1962) Discrete variable methods in Ordinary Differential Equations. John Wiley, New York.
13. Herzberg, G. (1950) Spectra of Diatomic Molecules. Van Nostrand, Toronto.
14. Ixaru, L. Gr. and Micu, M. (1978) Topics in Theoretical Physics. Central Institute of Physics, Bucharest.
15. Ixaru, L. Gr. and Rizea, M. (1980) Comput. Phys. Commun. 19, 23.
16. Killingbeck, J. (1987) J. Phys. A, Math. Gen. 20, 1411.
17. Kobeissi, H. and Kobeissi, M. (1988a) J. Comput. Chem. 9, 844.
18. Kobeissi, H. and Kobeissi, M. (1988b) J. Comput. Phys. 77, 501.
19. Kobeissi, H., Kobeissi, M. and El-Hajj, Ali (1989) J. Phys. A, Math. Gen. 22, 287.
20. Kroes, G. J. (1992) Comput. Phys. Commun. 70, 41.
21. Lambert, J. D. and Watson, I. A. (1976) J. Inst. Math. Applies. 18, 189.
22. Landau, L. D. and Lifshitz, F. M. (1965) Quantum Mechanics. Pergamon, New York.
23. Lyche, T. (1972) Numer. Math. 19, 65.
24. Raptis, A. D. (1981) Comput. Phys. Commun. 24, 1.
25. Raptis, A. D. (1982) Computing 28, 373.
26. Raptis, A. D. (1983) Comput. Phys. Commun. 28, 427.
27. Raptis, A. D. (1984) Bull. Greek Math. Soc. 25, 113.
28. Raptis, A. D. and Allison, A. C. (1978) Comput. Phys. Commun. 14, 1.
29. Raptis, A. D. and Cash, J. R. (1987) Comput. Phys. Commun. 44, 95.
30. Simos, T. E. (1990) Numerical solution of ordinary differential equations with periodical solution, Doctoral Dissertation, National Technical University of Athens.
31. Simos, T. E. (1990b) J. Comput. Appl. Math. 30, 251.
32. Simos, T. E. (1991) IMA J. Numer. Anal. 11, 347.
33. Simos, T. E. (1992) Comput. Phys. Commun. 71, 32.
34. Simos, T. E. (1993) Physics Letters A 177, 345.
35. Simos, T. E. and Tougelidis, G. (1996) Computers and Chemistry 20, 397.
36. Simos, T. E. and Williams, P. S., Computers and Chemistry (in press).
37. Vanden Berghe, G., Fack, V. and De Meyer, H. E. (1989) J. Comput. Appl. Math. 29, 391.