Stability of Runge--Kutta methods in the numerical solution of equation u'(t) = au(t) + a0u([t])

Authors:
M. Z. Liu;M. H. Song;Z. W. Yang
Affiliations:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

This paper is concerned with the stability analysis of the Runge-Kutta methods for the equation u'(t) = au(t) + a0u([t]). The stability regions for the Runge-Kutta methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained and some numerical experiments are given.