Generalization of Gegenbauer Wavelet Collocation Method to the Generalized Kuramoto–Sivashinsky Equation

Abstract

Gegenbauer (Ultraspherical) wavelets operational matrices play an important role for numeric solution of differential equations. In this study, operational matrices of rth integration of Gegenbauer wavelets are presented and general procedures of these matrices are correspondingly given first time. The proposed method is based on the approximation by the truncated Gegenbauer wavelet series. Algebraic equation system has been obtained by using the Chebyshev collocation points and solved. Proposed method has been applied to the Generalized Kuramoto–Sivashinsky equation using quasilinearization technique. Numerical examples showed that the method proposed in this study demonstrates the applicability and the accuracy of the Gegenbauer wavelet collocation method.