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Oscillation of numerical solution in the Runge-Kutta methods for equation x′(t) = ax(t) + a 0 x([t])

Oscillation of numerical solution in the Runge-Kutta methods for equation x′(t) = ax(t) + a 0 x([t]) The paper deals with oscillation of Runge-Kutta methods for equation x′(t) = ax(t) + a 0 x([t]). The conditions of oscillation for the numerical methods are presented by considering the characteristic equation of the corresponding discrete scheme. It is proved that any nodes have the same oscillatory property as the integer nodes. Furthermore, the conditions under which the oscillation of the analytic solution is inherited by the numerical solution are obtained. The relationships between stability and oscillation are considered. Finally, some numerical experiments are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Oscillation of numerical solution in the Runge-Kutta methods for equation x′(t) = ax(t) + a 0 x([t])

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Publisher
Springer Journals
Copyright
Copyright © 2014 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-014-0434-4
Publisher site
See Article on Publisher Site

Abstract

The paper deals with oscillation of Runge-Kutta methods for equation x′(t) = ax(t) + a 0 x([t]). The conditions of oscillation for the numerical methods are presented by considering the characteristic equation of the corresponding discrete scheme. It is proved that any nodes have the same oscillatory property as the integer nodes. Furthermore, the conditions under which the oscillation of the analytic solution is inherited by the numerical solution are obtained. The relationships between stability and oscillation are considered. Finally, some numerical experiments are given.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Nov 6, 2014

References