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Numerical study of the variable-order fractional version of the nonlinear fourth-order 2D diffusion-wave equation via 2D Chebyshev wavelets

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Abstract

In this article, the 2D Chebyshev wavelets (CWs) are used for designing a proper procedure to solve the variable-order (VO) fractional version of the nonlinear fourth-order diffusion-wave (DW) equation. In the presented model, fractional derivatives are defined in the Caputo type. The \(\theta \)-weighted finite difference technique is utilized to approximate the VO time fractional derivative through a recursive algorithm. By expanding the unknown solution in terms of the 2D CWs and substituting in the recursive equation, a linear system of algebraic equation is obtained. The accuracy of the method is studied on some numerical example.

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Authors and Affiliations

  1. Faculty of Mathematics, Yazd University, Yazd, Iran

    M. Hosseininia

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

    M. H. Heydari

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

    Z. Avazzadeh

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

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Hosseininia, M., Heydari, M.H. & Avazzadeh, Z. Numerical study of the variable-order fractional version of the nonlinear fourth-order 2D diffusion-wave equation via 2D Chebyshev wavelets. Engineering with Computers 37, 3319–3328 (2021). https://doi.org/10.1007/s00366-020-00995-z

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