A Reliable Approach of Ramadan Group Integral and Projected Differential Transform Methods to System of Nonlinear Partial Differential Equations

Abstract

In this paper, a hybrid method is presented via  combination of the Ramadan Group Integral method (RGITM) with method of Projected Differential Transform(PDTM) for the purpose of solving nonlinear partial differential equations systems. The method's goal is to produce analytical solutions in series form. In comparison to existing methods, the suggested method makes handling such partial differential equations simple. The outcome demonstrated the method's effectiveness, accuracy, and validity. The technique can be easily applied to a wide variety of nonlinear issues, and it has the potential to both reduce the amount of computation required and deal with the flaw brought about by the nonlinear components that cannot be resolved by employing recognized integral transforms. Examples will be looked at to help illustrate the proposed analysis