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

Author

Listed:
  • Azam Zahrani
  • Mashaallah Matinfar
  • Mostafa Eslami

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.

Suggested Citation

  • Azam Zahrani & Mashaallah Matinfar & Mostafa Eslami, 2022. "Bivariate Chebyshev Polynomials to Solve Time‐Fractional Linear and Nonlinear KdV Equations," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:6554221
    DOI: 10.1155/2022/6554221
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    References listed on IDEAS

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