Advanced Mathematical Models & Applications
Advanced Mathematical Models & Applications is a peer-reviewed, open access journal meant to publish original and significant results and articles in all areas of mathematical modeling and their applications. The aim of this Journal is to bring together researchers and practitioners from academia and industry to establishing new collaborations in this area. The Journal will consider for publication also review articles, literature reviews, correspondence concerning views and information published in previous issues.
Kharrat-Toma Perturbation Method for Solving Linear and Nonlinear Klein- Gordon Equations
- Published: 03-08-2025
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In this paper, we combine the Kharrat-Toma transform and the homotopy perturbation method for solving linear and nonlinear Klein-Gordon equations. Since the Klein-Gordon is two-variable equation, we first generalize the Kharrat-Toma transform to two-dimensional state. Then, we solve the linear Klein-Gordon equation only using the Kharrat-Toma transform and inverse Kharrat-Toma transform. Moreover, to solve the nonlinear Klein-Gordon equation, we combine the Kharrat-Toma transform with the homotopy perturbation method and obtain an approximate solution for it. Finally, we give some examples for both cases and compute the error of the approximate solutions.
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