A family of hybrid eighth order methods with minimal phase-lag for the numerical solution of the Schrödinger equation and related problems

International Journal of Modern Physics C

Volumn 11, Issue 2, 2000, Pages 415-437

  Avdelas, G ^a,c   Konguetsof, A ^b   Simos, T E ^b,c  

^a TECHNICAL UNIVERSITY OF CRETE   (Greece)

^b DEMOCRITUS UNIVERSITY OF THRACE   (Greece)

^c NONE   (Greece)

Author keywords

Algebraic Order; Hybrid Methods; Interval of Periodicity; Periodic Initial Value Problems; Phase Lag; Schr dinger Equation; Wave Equation

Indexed keywords

EID: 0034396254     PISSN: 01291831     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129183100000365     Document Type: Article

References (27)

1. L. D. Landau and F. M. Lifshitz, Quantum Mechanics (Pergamon, New York, 1965).
2. I. Prigogine and S. Rice eds., Advances in Chemical Physics Vol. 93: New Methods in Computational Quantum Mechanics (John Wiley & Sons, 1997).
3. T. E. Simos, J. Comput. Appl. Comm. 39, 89 (1992).
4. J. D. Lambert and I. A. Watson, J. Inst. Math. Appl. 18, 189 (1976).
5. L. Bruca and L. Nigro, Int. J. Num. Meth. Eng. 15, 685 (1980).
6. M. M. Chawla and P. S. Rao, J. Comp. Appl. Math. 11, 277 (1984).
7. M. M. Chawla and P. S. Rao, J. Comp. Appl. Math. 15, 329 (1986).
8. M. M. Chawla, P. S. Rao, and B. Neta, J. Comp. Appl. Math. 16, 233 (1986).
9. M. M. Chawla and P. S. Rao, J. Comp. Appl. Math. 16, 365 (1987).
10. J. P. Coleman, IMA J. Num. Anal. 9, 145 (1989).
11. T. E. Simos and A. D. Raptis, Computing 45, 175 (1990).
12. T. E. Simos, J. Comp. Phys. 108, 175 (1993).
13. G. Avdelas and T. E. Simos, Comp. Math. Appl. 31, 69 (1996).
14. G. Avdelas and T. E. Simos, Comp. Math. Appl. 31, 85 (1996).
15. T. E. Simos, Comp. Chem. 22, 433 (1998).
16. T. E. Simos, Numerical solution of ordinary differential equations with periodical solution, Doctoral Dissertation, National Technical University of Athens.
17. R. M. Thomas, BIT 24, 225 (1984).
18. T. E. Simos and G. Tougelidis, Comp. Chem. 20, 397 (1996).
19. E. Haker, S. P. Norset, and G. Wanner, Solving Ordinary Differential Equations I (Nonstiff Problems), 2nd ed. (Springer-Verlag, Berlin, 1993).
20. A. C. Allison, J. Comp. Phys. 6, 378 (1970).
21. R. B. Berstein, A. Dalgarno, H. Massey, and I. C. Percival, Proc. Roy. Soc. London-Ser. A 274, 427 (1963).
22. R. B. Berstrein, J. Chem. Phys. 33, 795 (1960).
23. A. D. Raptis and J. R. Cash, Comp. Phys. Comm. 36, 113 (1985).
24. T. E. Simos, Int. J. Mod. Phys. C 7, 825 (1996).
25. T. E. Simos, Int. J. Mod. Phys. C 9, 271 (1998).
26. T. E. Simos, Int. J. Mod. Phys. C 9, 1055 (1998).
27. P. J. van der Houwen and B. P. Sommeijer, SIAM J. Num. Anal. 24, 595 (1987).