New Approach for Solving (2+1)-Dimensional Differential Equation

Abstract

This article presents an exact analysis solution for (2+1) dimensional differential equations by using new approach based on coupled method via LA-transform with decomposition method to overcome the computational difficulties. Convergence of series solution has been discussed with two illustrated examples, and the method has shown a high-precision, fast approach to solve non-linear (2+1) dimensional PDEs with initial conditions, there is no need any discretization of domain or assumption for a small parameter to be present in the problem. The steps of suggested method are easy implemented, high accuracy and a rapid convergence to the exact solution compared with other methods can be used to solve this type of PDEs.

Efficient Modification of the Decomposition Method for Solving a System of PDEs

“…The linear unknown function ( ) ( ) can be decomposed by infinite series of components, illustrated in equation ( 4), and should be decomposed infinite series illustrated in equation (5).…”

“…The systems of partial differential equations (PDEs) have been used to describe many important models in real life, such as contamination, distribution of shallow water, heat, wave's contamination, and the chemical reactiondistribution model [1][2][3][4]. The general ideas and key characteristics of these systems are generally applicable [5]. In recent years, many authors have focused on solving the nonlinear systems of PDEs using various methods, such as Homotopy analysis method (HAM) [6], variational iteration method (VIM) [7], differential transform method (DTM) [8], Homotopy ISSN: 0067-2904…”

Design an efficient neural network for solving steady state problems

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