Solution of two dimensional nonlinear sine-gordon equation by using the reduced differential transform method

Abstract

In this study, the reduced differential transform method (RDTM) was applied to solve two dimensional nonlinear sine-Gordon equation subject to the appropriate initial conditions arising in various physical models. This method provides the solutions in the form of infinite series expansions which converge to their exact solutions with easily computed terms. Using the RDTM the exact solution can be obtained by constructing a recursive formula. Three test modeling problems from mathematical physics, nonlinear Sine-Gordon equations are considered to verify the efficiency, accuracy and convergence of the proposed method. Moreover, Solutions obtained by RDTM are in close conformity with the solutions of earlier studies in the review of the literatures and the results obtained shows that the RDTM technique is highly accurate, efficient, convenient, converge and require less effort in comparison to the other analytical and numerical methods such as DTM. Also, results indicate that the introduced method is promising for solving other type of linear and nonlinear partial differential equations.