Triple Sumudu Transform With Iterative Method For Solving Two-Dimensional Nonlinear Coupled Sine-Gordon Equations

Abstract

This thesis deals with finding exact analytical solution of two-dimensional nonlinear coupled Sine Gordon equation subjected to initial and boundary conditions using triple Sumudu transform with iterative method. It is aimed to obtain exact solution for two-dimensional nonlinear coupled Sine Gordon equation. Description of this analytical iterative methods and their convergence properties has been presented. Exact solution were obtained using the convergence series form and presented in the form of graphs. The solution of the nonlinear part of the coupled equations was solved a successive iterative method. The applied methods are powerful and efficient for solving the problem under consideration. The efficiency of the proposed methods was demonstrated by solving two different test problems. Illustrative examples were taken from Mathematical Physics problems to demonstrate the applicability and efficiency of the method. Finally we came to the conclusion that the proposed method are very promising, efficient and powerful than other methods in terms of providing exact solutions