Approximate Solutions to System of Nonlinear Partial Differential Equations using Reduced Differential Transform Method

Abstract

The main objective of this paper is to use the reduced differential transform method (RDTM) for finding the analytical approximate solutions for solving systems of nonlinear partial differential equations (NPDEs). The approximate solutions obtained by RDTM is verified by comparison with the exact solutions to show that the RDTM is quite accurate, reliable and can be applied for many other nonlinear partial differential equations. The method considers the use of the appropriate initial or boundary conditions and finds the solution without any discretization, transformation, or restrictive assumptions. This method is a simple and efficient method for solving the nonlinear partial differential equations. The numerical results show that this method is a powerful tool for solving systems of NPDEs. The analysis shows that our analytical approximate solutions converge very rapidly to the exact solutions.