Solution of Laplace Equation by Modified Differential Transform Method

Abstract

In this paper, we applied the modified two-dimensional differential transform method to solve Laplace equation. Laplace equation is one of Elliptic partial differential equations. These kinds of differential equations have specific applications models of physics and engineering. We consider four models with two Dirichlet and two Neumann boundary conditions. The simplicity of this method compared to other iteration methods is shown here. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.