Comparison Between Exact and Numerical Solutions Using Double Sumudu Decomposition Method and Finite Difference Method for Some Types of Partial Differential Equations

Abstract

In this thesis, we used the double Sumudu decomposition method to solve linear, nonlinear hyperbolic equations. This method is a combination of the decomposition method and double Sumudu transform. In order to check the applicability of this method, five examples are given. Theta-finite difference method is applied to solve singular linear, nonlinear hyperbolic equations and coupled system of hyperbolic equations, five examples are demonstrated to identify the accuracy of numerical results. The linear singular and coupled systems of fractional parabolic equations have been solved by the Crank-Nicolson method, two examples are applied to illustrate the method. Finally, we compared the exact and numerical solutions. In order to obtain the numerical solutions, programs of numerical solutions are written using MATLAB software.