A new modified Runge-Kutta-Nyström method with phase-lag of order infinity for the numerical solution of the Schrödinger equation and related problems

International Journal of Modern Physics C

Volumn 11, Issue 6, 2000, Pages 1195-1208

  Simos, T E ^a,c   Aguiar, Jesus Vigo ^b  

^a DEMOCRITUS UNIVERSITY OF THRACE   (Greece)

^b UNIVERSITY OF SALAMANCA   (Spain)

^c NONE   (Greece)

Author keywords

Oscillating Solutions; Phase Shift Problems; Phase Fitted; Phase Lag; Radial Schr dinger Equation; Resonance Problems; Runge Kutta Nystr m Methods; Scattering Problems

Indexed keywords

EID: 0034549225     PISSN: 01291831     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129183100001036     Document Type: Article

References (18)

1. L. Gr. Ixaru and M. Micu, Topics in Theoretical Physics, Central Institute of Physics, Bucharest, 1978.
2. L. Gr. Ixaru and M. Rizea, Comput. Phys. Commun. 19, 23 (1980).
3. L. D. Landau and F. M. Lifshitz, Quantum Mechanics (Pergamon, New York, 1965).
4. G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand, Toronto, 1950).
5. P. J. van der Houwen and B. P. Sommeijer, SIAM J. Numer. Anal. 24, 595 (1987).
6. J. R. Cash and A. D. Raptis, Comput. Phys. Commun. 33, 299 (1984).
7. J. R. Cash, A. D. Raptis, and T. E. Simos, J. Comput. Phys. 91, 413 (1990).
8. L. D. Lambert and I. A. Watson, J. Inst. Math. Applics. 18, 189 (1976).
9. P. Henrici, Discrete Variable Methods in Ordinary Differential Equations (John Wiley and Sons, New York, 1962).
10. R. M. Thomas, BIT 24, 225 (1984).
11. T. E. Simos, Numerical Solution of Ordinary Differential Equations with Periodical Solution, Doctoral Dissertation, National Technical University of Athens, 1990.
12. T. E. Simos, Int. J. Mod. Phys. C 7, 33 (1996).
13. T. E. Simos, Int. J. Mod. Phys. C 7, 825 (1996).
14. T. E. Simos, Int. J. Mod. Phys. C 9, 271 (1998).
15. T. E. Simos, Int. J. Mod. Phys. C 9, 1055 (1998).
16. T. E. Simos and P. S. Williams, Int. J. Mod. Phys. C 10, 830 (1999).
17. E. Fehlberg, "Classical eighth and lower-order Runge-Kutta-Nyström formulas with stepsize control for special second order differential equations," NASA Technical Report, NASA TR R-381, Washington, 1972.
18. E. Stiefel and D. G. Bettis, Numer. Math. 13, 154 (1969).