Numerical oscillation and non-oscillation analysis of the mixed type impulsive differential equation with piecewise constant arguments

Abstract

AbstractThe purpose of this paper is to study oscillation and non-oscillation of Runge-Kutta methods for linear mixed type impulsive differential equations with piecewise constant arguments. The conditions for oscillation and non-oscillation of numerical solutions are obtained. Also conditions under which Runge-Kutta methods can preserve the oscillation and non-oscillation of linear mixed type impulsive differential equations with piecewise constant arguments are obtained. Moreover, the interpolation function of numerical solutions is introduced and the properties of the interpolation function is discussed. It turns out that the zeros of the interpolation function converge to ones of the analytic solution with the same order of accuracy as that of the corresponding Runge-Kutta method. To confirm the theoretical results, the numerical examples are given.Keywords: oscillationnumerical solutionRunge-Kutta methodsimpulsive delay differential equationspiecewise constant argumentsDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.