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


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Seçer A. , Özdemir N.

ADVANCES IN DIFFERENCE EQUATIONS, vol.2019, no.1, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2019 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.1186/s13662-019-2297-8
  • Title of Journal : ADVANCES IN DIFFERENCE EQUATIONS
  • Keywords: Galerkin method, Gegenbauer wavelets, KdV-Burgers-Kuramoto (KBK) equation, Operational matrix of integration, VOLTERRA INTEGRAL-EQUATIONS, GALERKIN METHOD, NUMERICAL-SOLUTION

Abstract

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.