Explicit Runge-Kutta methods for initial value problems with oscillating solutions

Journal of Computational and Applied Mathematics

Volumn 76, Issue 1-2, 1996, Pages 195-212

  Calvo, M ^a   Franco, J M ^a   Montijano, J I ^a   Randez L ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Dispersion and dissipation errors; Periodic initial value problems; Runge Kutta methods

Indexed keywords

ERROR ANALYSIS; LINEAR ALGEBRA; MATHEMATICAL MODELS; NUMERICAL METHODS; PARAMETER ESTIMATION;

DISPERSION ERRORS; DISSIPATION ERRORS; LOCAL ERROR ESTIMATOR; OSCILLATING SOLUTIONS; PERIODIC INITIAL VALUE PROBLEMS; RUNGE KUTTA METHODS;

DIFFERENTIAL EQUATIONS;

EID: 0030381198     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(96)00103-3     Document Type: Article

References (13)

1. L. Brusa and L. Nigro, A one step method for direct integration of structural dynamic equations, Internat. J. Numer. Methods Eng. 15 (1980) 685-699.
2. J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations (Runge-Kutta and General Linear Methods) (Wiley, New York, 1987).
3. M. Calvo, J.I. Montijano and L. Rández, A polyvalent Runge-Kutta triple, Appl. Numer. Math. 15 (1994) 13-26.
4. E. Fehlberg, Classical fifth, sixth, seventh and eighth order Runge-Kutta formulas with stepsize control, NASA Tech. report R-287 1968.
5. E. Hairer, S.P. Norsett and G. Wanner, Solving Ordinary Differential Equations I. Non-stiff Problems (Springer, Berlin, 1987).
6. F.Q. Hu, M.Y. Hussaini and J.L. Manthey, Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics, J. Comput. Phy. 124 (1996) 177-191.
7. P.J. Prince and J.R. Dormand, High order embedded Runge-Kutta formulae, J. Comput. Appl. Math. 7 (1981) 67-75.
8. P.W. Sharp, J.M. Fine and K. Burrage, Two-stage and three-stage diagonally implicit Runge-Kutta-Nyström methods of orders three and four, IMA J. Numer. Anal. 10 (1990) 489-504.
9. A.B. Sideris and T.E. Simos, A low-order embedded Runge-Kutta method for periodic initial-value problems, J. Comput. Appl. Math. 44 (1992) 235-244.
10. P.J. Van der Houwen and B.P. Sommeijer, Explicit Runge-Kutta (Nyström) methods with reduced phase errors for computing oscillating solutions, SIAM J. Numer. Anal. 24 (1987) 595-617.
11. P.J. Van der Houwen and B.P. Sommeijer, Phase-lag analysis of implicit Runge-Kutta methods, SIAM J. Numer. Anal. 26 (1989) 214-229.
12. P.J. Van der Houwen and B.P. Sommeijer, Diagonally implicit Runge-Kutta-Nyström methods for oscillatory problems, SIAM J. Numer. Anal. 26 (1989) 414-429.
13. P.J. Van der Houwen, B.P. Sommeijer, K. Strehmel and R. Weiner, On the numerical integration of second-order initial value problems with a periodic forcing function, Tech. Report NM-R8604, Center for Mathematics and Computer Science, Amsterdam, The Netherlands, 1986.