MODIFIED HOMOTOPY PERTURBATION METHODS FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS

Homotopy perturbation method can be widely accepted for approximating or accurately solving nonlinear differential equations due to its generality and ease of use. Rational homotopy perturbation method and Rational biparameter homotopy perturbation method are two extensions of homotopy perturbation method which can improve the accuracy of the solution. In this paper, the algorithm steps of these two derived methods are introduced, meanwhile, the approximate solutions of Burgers equation and Gardner equation are obtained. Absolute errors of these two methods in solving partial differential equations are calculated and described to verify the effectiveness of the methods.