A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators

Journal of Computational and Applied Mathematics

Volumn 161, Issue 2, 2003, Pages 283-293

  Franco, J M ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Adapted RKN methods; Embedded pairs; Oscillatory problems

Indexed keywords

ALGEBRA; CODES (SYMBOLS); COMPUTER SIMULATION; INTEGRATION; PERTURBATION TECHNIQUES;

PERTURBATED OSCILLATORS;

OSCILLATORS (ELECTRONIC);

MATHEMATICAL ANALYSIS; OSCILLATION;

EID: 0242624843     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.03.002     Document Type: Article

References (17)

1. Avdelas G. Simos T.E. Vigo-Aguiar J. An embedded exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation and related periodic initial-value problems Comput. Phys. Commun. 131 2000 52-67
2. Bettis D.G. Numerical integration of products of Fourier and ordinary polynomials Numer. Math. 14 1970 421-434
3. Bettis D.G. Runge-Kutta algorithms for oscillatory problems J. Appl. Math. Phys. (ZAMP) 30 1979 699-704
4. Dormand J.R. El-Mikkawy M.E.A. Prince P.J. Families of Runge-Kutta-Nyström formulae IMA J. Numer. Anal. 7 1987 235-250
5. Franco J.M. Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators Comput. Phys. Commun. 147 2002 770-787
6. J.M. Franco, Embedded pairs of explicit ARKN methods for the numerical integration of perturbed oscillators, in: Proceedings of the 2002 Conference on Computational and Mathematical Methods on Science and Engineering, Vol. I, Alicante, 2002, pp. 92-101.
7. Franco J.M. An embedded pair of exponentially fitted explicit Runge-Kutta methods J. Comput. Appl. Math. 149 2002 407-414
8. Franco J.M. Palacián J.F. High order adaptive methods of Nyström-Cowell type J. Comput. Appl. Math. 81 1997 115-134
9. García A. Martín P. González A.B. New methods for oscillatory problems based on classical codes Appl. Numer. Math. 42 2002 141-157
10. González A.B. Martín P. Farto J.M. A new family of Runge-Kutta type methods for the numerical integration of perturbed oscillators Numer. Math. 82 1999 635-646
11. Hairer E. Nørsett S.P. Wanner S.P. Solving Ordinary Differential Equations I, Nonstiff Problems 1993 Springer Berlin
12. Jain M.K. A modification of the Stiefel-Bettis method for nonlinear damped oscillators BIT 28 1998 302-307
13. Paternoster B. Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials Appl. Numer. Math. 28 1998 401-412
14. Simos T.E. An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions Comput. Phys. Commun. 115 1998 1-8
15. Stiefel E. Bettis D.G. Stabilization of Cowell's Method Numer. Math. 13 1969 154-175
16. Vanden Berghe G. De Meyer H. Van Daele M. Van Hecke T. Exponentially-fitted explicit Runge-Kutta methods Comput. Phys. Commun. 123 1999 7-15
17. Vanden Berghe G. De Meyer H. Van Daele M. Van Hecke T. Exponentially fitted Runge-Kutta methods J. Comput. Appl. Math. 125 2000 107-115