Approximate periodic solution for nonlinear jerk equation as a third‐order nonlinear equation via modified differential transform method. Issue 4 (2014)

• Record Type: Journal Article
• Is Part Of: Engineering computations. Volume 31:Issue 4(2014)
• Page Start: 622
• Page End: 633
• Publication Date: 2014
• Subjects: Jerk equation -- Modified differential transform method -- Third‐order nonlinear equation; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-02-2012-0024
• Languages: English
• ISSNs: 0264-4401

Abstract

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.