Optimizing a hybrid two-step method for the numerical solution of the schrödinger equation and related problems with respect to phase-lag

Journal of Applied Mathematics

Volumn 2012, Issue , 2012, Pages

  Simos, T E ^a,b  

^a KING SAUD UNIVERSITY   (Saudi Arabia)

^b UNIVERSITY OF PELOPONNESE   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84861088351     PISSN: 1110757X     EISSN: 16870042     Source Type: Journal    
DOI: 10.1155/2012/420387     Document Type: Article

References (33)

1. Hairer E., Lubich C., Wanner G., Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations 2006 2nd Springer Series in Computational Mathematics
2. Ixaru L. Gr., Rizea M., A numerov-like scheme for the numerical solution of the Schrdinger equation in the deep continuum spectrum of energies Computer Physics Communications 1980 19 1 23 27
3. Konguetsof A., Simos T. E., A generator of hybrid symmetric four-step methods for the numerical solution of the Schrdinger equation Journal of Computational and Applied Mathematics 2003 158 1 93 106 (Pubitemid 37106075)
4. Chawla M. M., Rao P. S., An explicit sixth-order method with phase-lag of order eight for y = f (t, y) Journal of Computational and Applied Mathematics 1987 17 3 365 368 (Pubitemid 17573782)
5. Sanz-Serna J. M., Calvo M. P., Numerical Hamiltonian Problems 1994 7 London, UK Chapman Hall xii+207
6. Zhu W., Zhao X., Tang Y., Numerical methods with a high order of accuracy applied in the quantum system Journal of Chemical Physics 1996 104 6 2275 2286 (Pubitemid 126747585)
7. Chiou J. C., Wu S. D., Open Newton-Cotes differential methods as multilayer symplectic integrators Journal of Chemical Physics 1997 107 17 6894 6898 (Pubitemid 127606956)
8. Simos T. E., A fourth algebraic order exponentially-fitted Runge-Kutta method for the numerical solution of the Schrdinger equation IMA Journal of Numerical Analysis 2001 21 4 919 931 (Pubitemid 33382102)
9. Simos T. E., Exponentially-fitted Runge-Kutta-Nystrm method for the numerical solution of initial-value problems with oscillating solutions Applied Mathematics Letters 2002 15 2 217 225
10. Tsitouras Ch., Simos T. E., Optimized Runge-Kutta pairs for problems with oscillating solutions Journal of Computational and Applied Mathematics 2002 147 2 397 409 (Pubitemid 35273996)
11. Kalogiratou Z., Monovasilis Th., Simos T. E., Symplectic integrators for the numerical solution of the Schrdinger equation Journal of Computational and Applied Mathematics 2003 158 1 83 92 (Pubitemid 37106074)
12. Kalogiratou Z., Simos T. E., Newton-Cotes formulae for long-time integration Journal of Computational and Applied Mathematics 2003 158 1 75 82 (Pubitemid 37106073)
13. Psihoyios G., Simos T. E., Trigonometrically fitted predictor-corrector methods for IVPs with oscillating solutions Journal of Computational and Applied Mathematics 2003 158 1 135 144 (Pubitemid 37106078)
14. Simos T. E., Famelis I. T., Tsitouras C., Zero dissipative, explicit Numerov-type methods for second order IVPs with oscillating solutions Numerical Algorithms 2003 34 1 27 40 (Pubitemid 38104695)
15. Simos T. E., Dissipative trigonometrically-fitted methods for linear second-order IVPs with oscillating solution Applied Mathematics Letters 2004 17 5 601 607
16. Tselios K., Simos T. E., Runge-Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics Journal of Computational and Applied Mathematics 2005 175 1 173 181 (Pubitemid 40046735)
17. Sakas D. P., Simos T. E., Multiderivative methods of eighth algebraic order with minimal phase-lag for the numerical solution of the radial Schrdinger equation Journal of Computational and Applied Mathematics 2005 175 1 161 172 (Pubitemid 40046734)
18. Psihoyios G., Simos T. E., A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions Journal of Computational and Applied Mathematics 2005 175 1 137 147 (Pubitemid 40046732)
19. Anastassi Z. A., Simos T. E., An optimized Runge-Kutta method for the solution of orbital problems Journal of Computational and Applied Mathematics 2005 175 1 1 9 (Pubitemid 40046723)
20. Simos T. E., Closed Newton-Cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problems Applied Mathematics Letters 2009 22 10 1616 1621
21. Stavroyiannis S., Simos T. E., Optimization as a function of the phase-lag order of nonlinear explicit two-step P -stable method for linear periodic IVPs Applied Numerical Mathematics 2009 59 10 2467 2474
22. Simos T. E., Exponentially and trigonometrically fitted methods for the solution of the Schrdinger equation Acta Applicandae Mathematicae 2010 110 3 1331 1352
23. Simos T. E., Williams P. S., A finite-difference method for the numerical solution of the Schrdinger equation Journal of Computational and Applied Mathematics 1997 79 2 189 205 (Pubitemid 127423245)
24. Simos T. E., Williams P. S., On finite difference methods for the solution of the Schrdinger equation Computers and Chemistry 1999 23 6 513 554 (Pubitemid 129587935)
25. Lambert J. D., Watson I. A., Symmetric multistep methods for periodic initial value problems Journal of the Institute of Mathematics and its Applications 1976 18 2 189 202
26. Ixaru L.Gr., Micu M., Topics in Theoretical Physics 1978 Bucharest, Romania Central Institute of Physics
27. Landau L. D., Lifshitz F. M., Quantum Mechanics 1965 New York, NY, USA Pergamon
28. Simos T. E., Williams P. S., A new Runge-Kutta-Nystrm method with phase-lag of order infinity for the numerical solution of the Schrdinger equation MATCH Communications in Mathematical and in Computer Chemistry 2002 45 123 137
29. Dormand J. R., Prince P. J., Runge-Kutta-Nystrom triples Computers Mathematics with Applications 1987 13 12 937 949
30. Dormand J. R., El-Mikkawy M. E. A., Prince P. J., High-order embedded Runge-Kutta-Nystrom formulae IMA Journal of Numerical Analysis 1987 7 4 423 430
31. Dormand J. R., El-Mikkawy M. E. A., Prince P. J., Families of Runge-Kutta-Nystrm formulae IMA Journal of Numerical Analysis 1987 7 2 235 250
32. Quinlan G. D., Tremaine S., Symmetric multistep methods for the numerical integration of planetary orbits Astronomical Journal 1990 100 5 1694 1700
33. Chawla M. M., Rao P. S., A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial value problemsII. Explicit method Journal of Computational and Applied Mathematics 1986 15 3 329 337 (Pubitemid 16640502)