Application of Sumudu Decomposition Method to Solve Nonlinear System of Partial Differential Equations

Abstract

We develop a method to obtain approximate solutions of nonlinear system of partial differential equations with the help of Sumudu decomposition method (SDM). The technique is based on the application of Sumudu transform to nonlinear coupled partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of three examples, and results of the present technique have close agreement with approximate solutions obtained with the help of Adomian decomposition method (ADM).

Implementation of the Homotopy Perturbation Sumudu Transform Method for Solving Klein-Gordon Equation

“…There are several analytical have been presented in the literature to solve fractional partial differential equations (FPDEs), such as the Fourier transform method [1], the fractional Greens function method [2], the Mellin transform method and the Laplace transform method [3] [4], the Sumudu transform method [5]. Recently, several numerical methods have been introduced for this purpose, such as: the homotopy perturbation method (HPM) has first proposed by He [6]- [8], the Modified homotopy perturbation method (MHPM) [9], the differential transform method (DTM) [10], the variational iteration method (VIM) [11] [12], the homotopy analysis method (HAM) [13] [14], the Sumudu decomposition method [15], the Adomian decomposition method [16] [17].…”

RETRACTED：Implementation of the Homotopy Perturbation Sumudu Transform Method for Solving Klein-Gordon Equation

“…Some of these analytical methods are the Fourier transform method [1], the fractional Green function method [2], the popular Laplace transform method [3] [4], the Sumudu transform method [5], the iteration method [4], the Mellin transform method and the method of orthogonal polynomials [3]. Some numerical methods are also popular, such as the homotopy perturbation method (HPM) [6]- [8], the modified homotopy perturbation method (MHPM) [9], the differential transform method (DTM) [10], the variational iteration method (VIM) [11] [12], the homotopy analysis method (HAM) [13] [14], the Sumudu decomposition method [15] and the Adomian decomposition method [16] [17].…”

Sumudu Decomposition Method for Solving Fuzzy Integro-Differential Equations

“…Therefore, most of the time, an approximate solution is required. There are also useful numerical schemes that can produce a numerical approximation to solutions for some problems [4,5].…”