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

[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.

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