A fourth-order diagonally implicit Runge-Kutta-Nyström method with dispersion of high order

Authors:
N. Senu;M. Suleiman;F. Ismail;M. Othman
Affiliations:
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Serdang, Selangor, Malaysia;Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Serdang, Selangor, Malaysia;Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Serdang, Selangor, Malaysia;Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Selangor, Malaysia
Venue:
ASM'10 Proceedings of the 4th international conference on Applied mathematics, simulation, modelling
Year:
2010

Citing 6
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Abstract

A new diagonally implicit Runge-Kutta-Nyström (RKN) method is developed for the integration of initial-value problems for second-order ordinary differential equations possessing oscillatory solutions. Presented is a formula which is three-stage fourth-order with high order of dispersion and 'small' principal local truncation error terms. This new method is more accurate when compared with current methods of similar type for the numerical integration of second-order differential equations with periodic solutions, using constant step size.