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A numerical scheme to solve a class of two-dimensional nonlinear time-fractional diffusion equations of distributed order

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A Correction to this article was published on 19 February 2021

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Abstract

This article is devoted to obtain the numerical solution for a class of nonlinear two-dimensional distributed-order time-fractional diffusion equations. We discretize the problem by using a finite difference scheme in the time direction. Then, we solve the discretized nonlinear problem by a collocation approach based on the Legendre polynomials. The numerical algorithm is fully described and convergence analysis of the scheme is evaluated. Finally, few numerical implementations are presented to highlight the flexibility and the convergence rate of this method.

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Acknowledgements

We would like thank the anonymous reviewers for carefully reading this work and their insightful comments and suggestions that helped improve the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran

    A. Babaei, H. Jafari & S. Banihashemi

  2. Department of Mathematical Sciences, University of South Africa, UNISA0003, Pretoria, South Africa

    H. Jafari

  3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 110122, Taiwan

    H. Jafari

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  1. A. Babaei
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  3. S. Banihashemi
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Correspondence to H. Jafari.

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Babaei, A., Jafari, H. & Banihashemi, S. A numerical scheme to solve a class of two-dimensional nonlinear time-fractional diffusion equations of distributed order . Engineering with Computers 38, 2169–2181 (2022). https://doi.org/10.1007/s00366-020-01185-7

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