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.