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Highly accurate technique for solving distributed-order time-fractional-sub-diffusion equations of fourth order

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Abstract

This paper presents a new method for calculating the numerical solution of distributed-order time-fractional-sub-diffusion equations (DO-TFSDE) of fourth order. The method extends the shifted fractional Jacobi (SFJ) collocation scheme for discretizing both the time and space variables. The approximate solution is expressed as a finite expansion of SFJ polynomials whose derivatives are evaluated at the SFJ quadrature points. The process yields a system of algebraic equations that are solved analytically. The new method is compared with alternative numerical algorithms when solving different types of DO-TFSDE. The results show that the proposed method exhibits superior accuracy with an exponential convergence rate.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic, University (IMSIU), Riyadh, Saudi Arabia

    M. A. Abdelkawy & Mohammed M. Babatin

  2. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

    M. A. Abdelkawy

  3. UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Porto, Portugal

    António M. Lopes

Authors
  1. M. A. Abdelkawy
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  2. Mohammed M. Babatin
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  3. António M. Lopes
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Correspondence to António M. Lopes.

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Communicated by Agnieszka Malinowska.

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Abdelkawy, M.A., Babatin, M.M. & Lopes, A.M. Highly accurate technique for solving distributed-order time-fractional-sub-diffusion equations of fourth order. Comp. Appl. Math. 39, 65 (2020). https://doi.org/10.1007/s40314-020-1070-7

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  • DOI: https://doi.org/10.1007/s40314-020-1070-7

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