Accelerated HPSTM: An efficient semi-analytical technique for the solution of nonlinear PDE’s

Nonlinear engineering: Modeling and application

article

Deepak Grover¹  Dinkar Sharma²  Prince Singh¹ 

[1] Department of Mathematics, Lovely Professional University;Department of Mathematics, Lyallpur Khalsa College

关键词: accelerated He’s polynomial;    nonlinear delay partial differential equation;    homotopy perturbation method;    Sumudu transforms;   

DOI  :  10.1515/nleng-2020-0019

来源: De Gruyter

【 摘 要 】

In this paper a novel technique i.e. accelerated homotopy perturbation Sumudu transformation method (AHPSTM), which is a hybrid of accelerated homotopy perturbation method and Sumudu transformation to obtain an approximate analytic solution of nonlinear partial differential equation (PDE) with proportional delay, is used. This approach is based on the new form of calculating He’s polynomial, which accelerates the convergence of the series solution. The series solutions obtained from the proposed method are found to converge rapidly to exact solution. In order to affirm the effectiveness and legitimacy of proposed method, the proposed technique is implemented on nonlinear partial differential equation (PDE) with proportional delay. The condition of convergence of series solution is analyzed. Moreover, statistical analysis has been performed to analyze the outcome acquired by AHPSTM and other semi-analytic techniques.

【 授权许可】

Unknown