Trigonometrically fitted predictor-corrector methods for IVPs with oscillating solutions

Journal of Computational and Applied Mathematics

Volumn 158, Issue 1, 2003, Pages 135-144

  Psihoyios, G ^a   Simos, T E ^b  

^a ANGLIA RUSKIN UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF PELOPONNESE   (Greece)

Author keywords

Adams Bashforth Moulton methods; Initial value problems (IVPs); Multistep methods; Numerical solution; Predictor corrector methods; Trigonometric fitting

Indexed keywords

COMPUTATIONAL METHODS; NUMERICAL METHODS; OSCILLATIONS;

PREDICTOR-CORRECTOR METHODS;

INITIAL VALUE PROBLEMS;

MATHEMATICAL METHOD;

EID: 0043287096     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(03)00481-3     Document Type: Article

References (20)

1. Dormand J.R. Prince P.J. A family of embedded Runge-Kutta formulae J. Comput. Appl. Math. 6 1980 19-26
2. Hairer E. Norset S.P. Wanner G. Solving Ordinary Differential Equations I, Nonstiff Problems 2nd Edition 1993 Springer Berlin
3. Ixaru L.Gr. Numerical Methods for Differential Equations and Applications 1984 Reidel Dordrecht, Boston, Lancaster
4. Konguetsof A. Simos T.E. On the construction of exponentially-fitted methods for the numerical solution of the Schrödinger equation J. Comput. Methods Sci. Eng. 1 2001 143-165
5. Lambert J.D. Numerical Methods for Ordinary Differential Systems 1991 Wiley Chichester
6. Landau L.D. Lifshitz F.M. Quantum Mechanics 1965 Pergamon New York
7. Lyche T. Chebyshevian multistep methods for ordinary differential equations Numer. Math. 10 1972 65-75
8. I. Prigogine, S. Rice (Eds.), Advances in Chemical Physics, Vol. 93: New Methods in Computational Quantum Mechanics, Wiley, New York, 1997.
9. G. Psihoyios, T.E. Simos, Exponentially and trigonometrically-fitted explicit advanced step-point (EAS) methods for IVPs with oscillating solution, Internat. J. Mod. Phys. C (2003), to appear.
10. Quinlan G.D. Tremaine S. Symmetric multistep methods for the numerical integration of planetary orbits Astron. J. 100 1990 1694-1700
11. Raptis A.D. Allison A.C. Exponential-fitting methods for the numerical solution of the Schrödinger equation Comput. Phys. Commun. 14 1978 1-5
12. L.F. Shampine, M.K. Gordon, Computer Solutions of Ordinary Differential Equations: The Initial Value Problem, W.H. Freeman, San Francisco, 1975.
13. T.E. Simos, Numerical solution of ordinary differential equations with periodical solution, Doctoral Dissertation, National Technical University of Athens, Greece, 1990 (in Greek).
14. T.E. Simos, in: A. Hinchliffe (Ed.), Atomic Structure Computations in Chemical Modelling: Applications and Theory, UMIST, The Royal Society of Chemistry, London, 2000, 38-142.
15. Simos T.E. Vigo-Aguiar J. On the construction of efficient methods for second order IVPs with oscillating solution Internat. J. Mod. Phys. C 10 2001 1453-1476
16. Simos T.E. Williams P.S. On finite difference methods for the solution of the Schrödinger equation Comput. Chem. 23 1999 513-554
17. Stiefel E. Bettis D.G. Stabilization of Cowell's method Numer. Math. 13 1969 154-175
18. Van Daele M. Vanden Berghe G. De Meyer H. Properties and implementation of r-Adams methods based on mixed-type interpolation Comput. Math. Appl. 30 1995 37-54
19. J. Vigo-Aguiar, Mathematical methods for the numerical propagation of satellite orbits, Doctoral Dissertation, University of Valladolid, Spain, 1993 (in Spanish).
20. Vigo-Aguiar J. Ferrandiz J.M. A general procedure for the adaptation of multistep algorithms to the integration of oscillatory problems SIAM J. Numer. Anal. 35 1998 1684-1708