Randomly generated grids and Laplace Transform for partial differential equations

Abstract

In this research work, we are solving partial differential equation(PDE’S). Partial differential equation solves through various method Like Analytics method, Numerical Method , Laplace transform and others, In this Paper, we arefocusing on solution of Randomly grids, Grids usually called meshes, there is no rule to fixed a mesh, Grids are based on problem and varies as per problems requirement. Numerical Solution using Finite difference method is based on grids. The idea of randomly generated meshes helps to decide the practicability and feasibility of such approaches. In this research, iterations and performance measured. Here is the solution by Laplace transformand Convergence to underlying the solutions.Solutions through randomly generated grids and Laplace Transform compared. Solution through Randomly grids are always better than Analytic, uniform meshes as well Laplace Transform methods. Which proves that randomly generated grids are better results than uniform meshes.