Convergence and Error Analysis of Series Solution of Nonlinear Partial Differential Equation

Nonlinear engineering: Modeling and application

article

Prince Singh¹  Dinkar Sharma² 

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

关键词: Homotopy perturbation method;    Sumudu transformation;    He’s polynomial;    Convergence analysis;    Error analysis;   

DOI  :  10.1515/nleng-2017-0113

来源: De Gruyter

【 摘 要 】

A hybrid method of Sumudu transforms and homotopy perturbation method (HPM) is used to solve nonlinear partial differential equation. Here the nonlinear terms are handled with He’s polynomial to obtain the series solution. But, for the authenticity of the obtained solution, the condition of convergence and uniqueness of the solution is derived. The facts are obtained in reference to convergence and error analysis of this solution. Finally, the established fact is supported by finding solution of two well known equations Newell-Whitehead Segel and Fisher’s equation.

【 授权许可】

Unknown