Numerical Stability and Oscillations of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments of Advanced Type

Numerical Stability and Oscillations of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments of Advanced Type

Year:    2013

Author:    Qi Wang

Communications in Mathematical Research , Vol. 29 (2013), Iss. 2 : pp. 131–142

Abstract

For differential equations with piecewise constant arguments of advanced type, numerical stability and oscillations of Runge-Kutta methods are investigated. The necessary and sufficient conditions under which the numerical stability region contains the analytic stability region are given. The conditions of oscillations for the Runge-Kutta methods are obtained also. We prove that the Runge-Kutta methods preserve the oscillations of the analytic solution. Moreover, the relationship between stability and oscillations is discussed. Several numerical examples which confirm the results of our analysis are presented.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2013-CMR-19018

Communications in Mathematical Research , Vol. 29 (2013), Iss. 2 : pp. 131–142

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    numerical solution Runge-Kutta method asymptotic stability oscillation.

Author Details

Qi Wang