A CONTINUOUS RUNGE-KUTTA-NYSTR¨OM COLLOCATION METHOD WITH TRIGONOMETRIC COEFFICIENTS FOR PERIODIC INITIAL VALUE PROBLEMS

J. O. EHIGIE, S. N. JATOR, S. A. OKUNUGA

Abstract


In this paper, we construct a two-step continuous multistep scheme of Numerov type with two off-grid points via multistep collocation technique. With the generation of several discrete multistep schemes of Numerov type, we show that these discrete methods represent a practical four stage Runge-Kutta- Nystrom Collocation Method (RKNCM) with trigonometric coefficients. A detailed analysis of the method such as the stability plots as well as the phase properties of the RKNCM are investigated and presented. Numerical experiments are carried out to illustrate the high effectiveness of the RKNCM compared with some recent methods in the literature.

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