A Four-stage Implicit Runge-Kutta-Nyström Method with Variable Coefficients for Solving Periodic Initial Value Problems

Japan Journal of Industrial and Applied Mathematics

Volumn 16, Issue 1, 1999, Pages 25-46

  Ozawa, Kazufumi ^a  

^a TOHOKU UNIVERSITY   (Japan)

Author keywords

Periodic initial value problems; Runge kutta nystr m method; Trigonometric order

Indexed keywords

EID: 0002966890     PISSN: 09167005     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03167523     Document Type: Article

References (11)

1. W. Gautschi, Numerical integration of ordinary differential equations based on trigonometric polynomials. Numer. Math., 3 (1961), 381-397.
2. E. Hairer and G. Wanner, A theory for Nyström methods. Numer. Math., 25 (1976), 383-400.
3. E. Hairer, S.P. Nørsett and G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems (2nd ed.). Springer-Verlag, 1993.
4. T.E. Hull, W.H. Enright, B.M. Fellen and A.E. Sedgwick, Comparing numerical methods for ordinary differential equations. SIAM J. Numer. Anal., 9 (1972), 603-607.
5. K. Ozawa, Fourth order P-stable block method for solving the differential equations y″ = f(x, y). Numerical Analysis of Ordinary Differential Equations and Its Applications (eds. T. Mitsui and Y. Shinohara), World Scientific, Singapore, 1995, 29-41.
6. L.F. Shampine, Numerical Solution of Ordinary Differential Equations. Chapman & Hall, 1994.
7. T.E. Simos, Modified Runge-Kutta-Fehlberg methods for periodic initial-value problems. Japan J. Indust. Appl. Math., 12 (1995), 109-122.
8. P.J. van der Houwen and B.P. Sommeijer, Runge-Kutta (-Nyström) methods with reduced phase errors for computing oscillating solutions. SIAM J. Numer. Anal., 24 (1987), 595-617.
9. 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.
10. P.J. van der Houwen, B.P. Sommeijer and N.H. Cong, Stability of collocation-based Runge-Kutta-Nyström Methods. BIT, 31 (1991), 469-489.
11. J. Vanthournout, H. De Meyer and G.V. Berghe, Multistep methods for ordinary differential equations based on algebraic and first order trigonometric polynomials. Computational Ordinary Differential Equations (eds. J.R. Cash and I. Gladwell), Oxford, New York, 1992, 61-72.