Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/6554221 |
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| Summary: | 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. |
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| ISSN: | 2314-4785 |