Phase-fitted collocation-based Runge-Kutta-Nystrom method

Applied Numerical Mathematics

Volumn 35, Issue 4, 2000, Pages 339-355

  Paternoster, B ^a  

^a UNIVERSITY OF SALERNO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS; RUNGE KUTTA METHODS;

RUNGE-KUTTA-NYSTROM METHOD;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 0034509539     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(99)00143-9     Document Type: Article

References (27)

1. Brankin R.W., Gladwell I., Dormand J.R., Prince P.J., Seward W.L. ALGORITHM 670, A Runge-Kutta Nyström code. ACM Trans. Math. Software. 15:(1):1989;31-40.
2. Burrage K. Parallel and Sequential Methods for Ordinary Differential Equations. 1995;Clarendon Press, Oxford.
3. Brunner H., van der Houwen P.J. The Numerical Solution of Volterra Equations. CWI Monographs. 3:1996;North-Holland, Amsterdam.
4. Cafaro M., Paternoster B. Analysis of stability of rational approximations through computer algebra. Ganzha V.G., Mayr E.W., Vorozhtsov E.V. Computer Algebra in Scientific Computing CASC-99 (Munich 1999). 1999;25-36 Springer-Verlag, Berlin.
5. Coleman J.P. Rational approximations for the cosine function; P-acceptability and order. Numer. Algorithms. 1992;143-158.
6. ′′=f(x,y) . IMA J. Numer. Anal. 16:1996;179-199.
7. Crisci M.R., Paternoster B., Russo E. Fully parallel Runge-Kutta Nyström methods for ODEs with oscillating solutions. Appl. Numer. Math. 11:1993;143-158.
8. Crisci M.R., Paternoster B. Parallel Runge-Kutta Nyström methods. Ricerche Mat. 47:1998;125-147.
9. Franco J.M. An explicit hybrid method of Numerov type for second-order periodic initial value problems. J. Comput. Appl. Math. 59:1995;79-90.
10. Hairer E., Norsett S.P., Wanner G. Solving Ordinary Differential Equations I. Nonstiff Problems. Springer Series in Computational Mathematics. 8:1987;Springer-Verlag, Berlin.
11. Huu Cong Nguyen. Note on the performance of direct and indirect Runge-Kutta-Nyström methods. J. Comput. Appl. Math. 45:1993;347-355.
12. L.Gr. Ixaru, Exponential-fitted methods: problems and applications, Private communication, June 1999.
13. ′′=f(x,y) . J. Comput. Appl. Math. 106:1999;87-98.
14. Ixaru L.Gr., Rizea M. A Numerov-like scheme for the numerical solution of the Schrödinger equation. Comput. Phys. Commun. 19:1980;23-27.
15. Ixaru L.Gr., Vanden Berghe G., De Meyer H., Van Daele M. Four-step exponential-fitted methods for nonlinear physical problems. Comput. Phys. Comm. 100:1997;71-80.
16. ′′=f(t,y) . BIT. 20:1980;215-222.
17. Paternoster B. Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials. Appl. Numer. Math. 28:1998;401-412.
18. Paternoster B., Cafaro M. Computation of the interval of stability of Runge-Kutta-Nyström methods. J. Symb. Comput. 25:(3):1998;383-394.
19. Petzold L.R., Jay L.O., Yen J. Numerical solution of highly oscillatory ordinary differential equations. Acta Numer. 1997;437-483.
20. Raptis A.D., Simos T.E. A four-step phase-fitted method for the numerical integration of second order initial-value problems. BIT. 31:1991;160-168.
21. Sanz-Serna J.M., Calvo M.P. Numerical Hamiltonian Problems. 1994;Chapman-Hall, London.
22. Simos T.E., Dimas E., Sideridis A.B. A Runge-Kutta-Nyström method for the numerical integration of special second-order periodic initial-value problems. J. Comput. Appl. Math. 51:1994;317-326.
23. van der Houwen P.J., Sommeijer B.P. Explicit Runge-Kutta(-Nyström) methods with reduced phase errors for computing oscillating solution. SIAM J. Numer. Anal. 24:1987;595-617.
24. van der Houwen P.J., Sommeijer B.P. Diagonally implicit Runge-Kutta Nyström methods for oscillatory problems. SIAM J. Numer. Anal. 26:1989;414-429.
25. van der Houwen P.J., Sommeijer B.P., Huu Cong Nguyen. Stability of collocation-based Runge-Kutta-Nyström methods, Report NM-R9016. 1990;Centre for Mathematics and Computer Science, Amsterdam.
26. van der Houwen P.J., Sommeijer B.P., Huu Cong Nguyen. Stability of collocation-based Runge-Kutta-Nyström methods. BIT. 31:1991;469-481.
27. van der Houwen P.J., Sommeijer B.P., Strehmel K., Weiner R. On the numerical integration of second order initial value problems with a periodic forcing function. Computing. 37:1986;195-218.