AN EFFICIENT NUMERICAL SOLUTION METHOD FOR NONLINEAR KLEIN-GORDON EQUATION VIA TAYLOR WAVELET METHOD

Authors : Nurcan Gücüyenen Kaymak, Yeşim Çiçek

Pages : 105-117

Doi:10.22531/muglajsci.1733279

View : 62 | Download : 187

Publication Date : 2025-12-31

Article Type : Research Paper

Abstract :The Klein–Gordon equation is of fundamental importance in mathematical physics, particularly due to its extensive applications in the analysis of solitonic phenomena, condensed matter systems, and the behavior of nonlinear wave dynamics. In this study, we develop a highly accurate numerical algorithm based on Taylor wavelets combined with the collocation technique, to approximate the solutions of nonlinear Klein-Gordon equations. An integration operational matrix is constructed and employed to transform the nonlinear Klein-Gordon initial–boundary value problem into an equivalent system of algebraic equations. One of the advantages of this method is that it does not require any restriction on domain discretization. This study also provides valuable insights into the underlying theoretical properties of the proposed method. To verify the reliability and accuracy of the proposed Taylor wavelet-based algorithm, a convergence analysis is performed. The method is then applied to four benchmark problems to further assess its effectiveness and computational performance. The comparison between the numerical and exact solutions demonstrates that the proposed method yields highly accurate results with minimal errors. All computations have been executed using MATLAB-2023b programming language.
Keywords : Sayısal çözüm, Taylor Dalgacığı, Doğrusal olmayan dalga, Hata, Yakınsama

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