An embedded 5(4) pair of modified explicit Runge Kutta methods for the numerical solution of the schrödinger equation

International Journal of Modern Physics C

Volumn 16, Issue 6, 2005, Pages 879-894

  Van De Vyver, Hans ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Coupled differential equations of schr dinger type; Embedded Runge Kutta methods; Explicit Runge Kutta methods; Phase shift problem; Variable stepsize algorithms

Indexed keywords

EID: 22944432161     PISSN: 01291831     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129183105007625     Document Type: Review

References (32)

1. T. E. Simos, Chemical Modeling-Applications and Theory, Vol. 1, Specialist Periodical Reports (The Royal Society of Chemistry, Cambridge, 2000), pp. 38-142.
2. T. E. Simos, Chemical Modeling-Applications and Theory, Vol. 2, Specialist Periodical Reports (The Royal Society of Chemistry, Cambridge, 2002), pp. 170-270.
3. T. E. Simos, Chemical Modeling-Applications and Theory, Vol. 3, Specialist Periodical Reports (The Royal Society of Chemistry, Cambridge, 2004), pp. 271-378.
4. M. M. Chawla, BIT 21, 190 (1981).
5. M. M. Chawla and P. S. Rao, J. Comput. Appl. Math. 11, 277 (1984).
6. A. Raptis and A. C. Allison, Comput. Phys. Comm. 14, 1 (1978).
7. L. Gr. Ixaru and M. Rizea, Comput. Phys. Comm. 19, 23 (1980).
8. A. D. Raptis and T. E. Simos, BIT 31, 160 (1991).
9. A. D. Raptis and J. R. Cash, Comput. Phys. Comm. 44, 95 (1987).
10. T. E. Simos, J. Math. Chem. 24, 443 (1998).
11. T. E. Simos and P. S. Williams, Int. J. Modern Phys. C 10, 839 (1999).
12. G. Avdelas, T. E. Simos and J. Vigo-Aguiar, Comput. Phys. Comm. 131, 52 (2000).
13. P. S. Williams and T. E. Simos, Int. J. Modern Phys. C 11, 785 (2000).
14. T. E. Simos, Int. J. Modern Phys. C11, 1115 (2000).
15. T. E. Simos and J. Vigo-Aguiar, Int. J. Modern Phys. C 11, 1195 (2000).
16. T. E. Simos and J. Vigo-Aguiar, Comput. Chem. 25, 275 (2001).
17. H. Van de Vyver, Comput. Phys. Comm. 166, 109 (2005).
18. G. Vanden Berghe, H. De Meyer, M. Van Daele and T. Van Hecke, Comput. Phys. Comm. 123, 7 (1999).
19. E. Hairer, S. P. Nørsett and G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems, 2nd edn. (Springer-Verlag Berlin, Heidelberg, New-York, 1993).
20. A. D. Raptis and J. R. Cash, Comput. Phys. Comm. 36, 113 (1985).
21. J. R. Dormand and P. J. Prince, J. Comp. Appl. Math. 6, 19 (1980).
22. G. Vanden Berghe, L. Gr. Ixaru and M. Van Daele, Comput. Phys. Comm. 140, 346 (2001).
23. G. Vanden Berghe, M. Van Daele and H. Van de Vyver, J. Comp. Appl. Math. 159, 217 (2003).
24. H. Van de Vyver, J. Comp. Appl. Math., in press (available online via ScienceDirect).
25. Ch. Tsitouras and T. E. Simos, J. Comp. Appl. Math. 147, 397 (2002).
26. R. B. Bernstein, J. Chem. Phys. 33, 795 (1960).
27. A. C. Allison, J. Comput. Phys. 6, 378 (1970).
28. A. M. Arthurs and A. Dalgarno, Proc. Roy. Soc. Ser. A 256, 540 (1960).
29. R. B. Bernstein, A. Dalgarno, H. Massey and I. C. Percival, Proc. Roy. Soc. Ser. A 274, 427 (1963).
30. W. A. Lester and R. B. Bernstein, J. Chem. Phys. 48, 4896 (1968).
31. W. A. Lester and R. B. Bernstein, Chem. Phys. Lett. 1, 207 (1967); Chem. Phys. Lett. (Errata) 1, 347.
32. B. R. Johnson, D. Secrest, W. A. Lester and R. B. Bernstein, Chem. Phys. Lett. 1, 396 (1967).