Sumudu transform HPM for Klein-Gordon and Sine-Gordon equations in one dimension from an analytical aspect

Abstract

In the present research work, a hybrid algorithm is introduced, which includes an integral transform “Sumudu Transform” and the well-known semi-analytical regime “Homotopy Perturbation Method” named as “Sumudu Transform Homotopy Perturbation Method (STHPM)” to evaluate the exact solution of Klein-Gordon and Sine-Gordon equations. The discussed equations in this research have a prominent role in sciences and engineering. The authenticity and efficacy of this regime are established via a comparison between approximated solutions and exact solutions. Convergence analysis is also provided, which affirms that the solution obtained from STHPM is convergent and unique in nature. The results obtained by STHPM are compared with exact solutions. 2D and 3D plots are also discussed. The present regime is a reliable technique to provide the exact solution to a wide category of non-linear PDEs in an easy way, without any need of discretization, complex computation, linearization, and it is also error-free.