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Numerical solution of variable-order space-time fractional KdV–Burgers–Kuramoto equation by using discrete Legendre polynomials

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Abstract

In this paper, a new version of the nonlinear space-time fractional KdV–Burgers–Kuramoto equation has been generated via the variable-order (VO) fractional derivatives defined in the Caputo type. A numerical method has been developed based on the discrete Legendre polynomials (LPs) and the collocation scheme for solving this equation. First, the solution of the problem is expanded in terms of the shifted discrete LPs. Then, this expansion and its derivatives, including the classical partial derivatives and the VO fractional partial derivatives are replaced in the equation. Eventually, the operational matrices of the shifted discrete LPs, including the classical derivatives and the VO fractional derivatives (which are derived in this study), and the collocation method are employed to convert the approximated problem into an algebraic system of equations. Some numerical results are given to illustrate the accuracy of the method.

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Authors and Affiliations

  1. Department of Mathematics, Shiraz University of Technology, Shiraz, Iran

    M. H. Heydari

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Z. Avazzadeh

  3. Engineering School (DEIM), University of Tuscia, Viterbo, Italy

    C. Cattani

Authors
  1. M. H. Heydari
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  2. Z. Avazzadeh
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  3. C. Cattani
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Correspondence to Z. Avazzadeh.

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Heydari, M.H., Avazzadeh, Z. & Cattani, C. Numerical solution of variable-order space-time fractional KdV–Burgers–Kuramoto equation by using discrete Legendre polynomials. Engineering with Computers 38 (Suppl 1), 859–869 (2022). https://doi.org/10.1007/s00366-020-01181-x

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