ئەز   Shrooq Mohammed Azzo

In this work, we use the homotopy analysis method (HAM) and combine it with the sumudu transform method (STM). This connection between the two methods is called the Sumudu homotopy analysis method (SHAM), and we use the method to solve generalized Hirota-Satsuma coupled kdv systems. And we compare the approximate solutions of this method with the Sumudu transform method. Comparison tables and graphics showed that SHAM is much closer than STM to the exact solution.

In this work, we take Adomian Decomposition Method (ADM) and combine it with Sumudu Transform method (STM). This connection between the two methods is called Sumudu-Decomposition Method (SDM), then use it to solve generalized HirotaSatsuma Coupled kdv (H-SC kdv) systems and also we applied the STM, to find the approximate solutions of system one. Then we compare the approximate solutions of the two way with exact solitary solutions. Clarifying the best way through tables and drawings, then discussing the reason for the changes taking place in the roads and which one is closest to the exact solution.

In this paper, we propose the Sumudu Homotopy perturbation Method (SHPM) to solve Generalized HirotaSatsuma coupled KdV systems. After comparing between approximate solution and the exact solution for the method with an approximate solution and the exact solution for the Sumudu Transform method (STM), we will see that the Sumudu Homotopypert urbationMethod is best than the Sumudu Transform method. In this work the differences between the methods it’s clear from the tables and figures. All numerical results were obtained using MATHEMATICA software utilizing all of the approaches.