An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation

Advances in Difference Equations

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[1] 0000 0001 2337 3561, grid.38575.3c, Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey;

关键词: Galerkin method;    Gegenbauer wavelets;    KdV-Burgers-Kuramoto (KBK) equation;    Operational matrix of integration;   

DOI  :  10.1186/s13662-019-2297-8

来源: publisher

【 摘 要 】

In this paper, our purpose is to present a wavelet Galerkin method for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation, which describes nonlinear physical phenomena and involves instability, dissipation, and dispersion parameters. The presented computational method in this paper is based on Gegenbauer wavelets. Gegenbauer wavelets have useful properties. Gegenbauer wavelets and the operational matrix of integration, together with the Galerkin method, were used to transform the time-fractional KBK equation into the corresponding nonlinear system of algebraic equations, which can be solved numerically with Newton’s method. Our aim is to show that the Gegenbauer wavelets-based method is efficient and powerful tool for solving the KBK equation with time-fractional derivative. In order to compare the obtained numerical results of the wavelet Galerkin method with exact solutions, two test problems were chosen. The obtained results prove the performance and efficiency of the presented method.

【 授权许可】

CC BY