Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations

Azam Zahrani, Mashaallah Matinfar, Mostafa Eslami and Arzu Akbulut

Journal of Mathematics, 2022, vol. 2022, 1-12

Abstract: This work concerns the numerical solutions of a category of nonlinear and linear time-fractional partial differential equations (TFPDEs) that are called time-fractional inhomogeneous KdV and nonlinear time-fractional KdV equations, respectively. The fractional derivative operators are of the Caputo type. Two-variable second-kind Chebyshev wavelets (SKCWs) are constructed using one-variable ones; then, utilizing corresponding integral operational matrices leads to an approximate solution to the problem under study. Also, it is found that the perturbation term tends to zero even if a finite number of the basis functions is adopted. To exhibit the applicability and efficiency of the proposed scheme, two models of the KdV equations are given.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6554221

DOI: 10.1155/2022/6554221

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