A Finite difference method using randomly generated grids as nonuniform meshes to solvethe partial differential equation

Abstract

This study presents the idea of randomly generated grids forsolving two-dimensional heat equation using finite difference method. The numerical solution of partial differential equation using finite difference method is based on meshes usually called grids. There is no universal principle for generating meshes, by using MATLAB and generating the Random grids. In this research, solution of heat equation using finite difference method over uniform and non-uniform called as randomly generated grids and various methods. The idea of using randomly generated meshes is compared by solution wise, iteration wise and time wise. It has been found that the results of randomly generated grids is best andfaster convergence. This research contributes method of using random meshes to
solve the partial differential equation.