Approximate periodic solution for nonlinear jerk equation as a third-order nonlinear equation via modified differential transform method

Abstract

Purpose

The nonlinear jerk equation is a third-order nonlinear equation that describes some physical phenomena and in general form is given by: x = J (x, x, x). The purpose of this paper is to employ the modified (MDTM) differential transform method (DTM) to obtain approximate periodic solutions of two cases of nonlinear jerk equation.

Design/methodology/approach

The approach is based on MDTM that is developed by combining DTM, Laplace transform and Padé approximant.

Findings

Comparison of results obtained by MDTM with those obtained by numerical solutions indicates the excellent accuracy of solution.

Originality/value

The MDTM is extended to determining approximate periodic solution of third-order nonlinear differential equations.

Citation

Mirzabeigy, A. and Yildirim, A. (2014), "Approximate periodic solution for nonlinear jerk equation as a third-order nonlinear equation via modified differential transform method", Engineering Computations, Vol. 31 No. 4, pp. 622-633. https://doi.org/10.1108/EC-02-2012-0024