Comparison and coupling of polynomials for Flierl-Petviashivili equation

Abstract

This paper outlines a comparison of the couplings of He’s and Adomian’s polynomials with correction functional of variational iteration method (VIM) to investigate a solution of Flierl-Petviashivili (FP) equation which plays a very important role in mathematical physics, engineering and applied sciences. These elegant couplings give rise to two modified versions of VIM which are very efficient in solving initial and boundary value problems of diversified nature. Moreover, we also introduces a new transformation which is required for the conversion of the Flierl-Petviashivili equation to a first order initial value problem and a reliable framework designed to overcome the difficulty of the singular point at x = 0. The proposed modified versions are applied to the reformulated first order initial value problem which gives the solution in terms of transformed variable. The desired series of solution is obtained by making use of the inverse transformation. It is observed that the modification based on He’s polynomials is much easier to implement and is more user friendly.