Preservation of oscillations of the Runge-Kutta method for equation x'(t)+ax(t)+a1x([t-1])=0

Authors:
M. Z. Liu;J. F. Gao;Z. W. Yang
Affiliations:
Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, PR China;School of Mathematical Sciences, Harbin Normal University, Harbin, 150025, PR China;Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, PR China and Science Research Center, The Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Techn ...
Venue:
Computers & Mathematics with Applications
Year:
2009

Citing 6
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Abstract

The paper deals with the preservation of oscillations of the Runge-Kutta method for equation x^'(t)+ax(t)+a"1x([t-1])=0. It is proved that oscillations of the analytic solution are preserved by the Runge-Kutta method. Special interpolation functions of the numerical solutions are given. It turns out that zeros of the interpolation function of the numerical solution converge to ones of the analytic solution with the same order of accuracy as that of the corresponding Runge-Kutta method. Some numerical experiments are presented.