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An efficient parametric finite difference and orthogonal spline approximation for solving the weakly singular nonlinear time-fractional partial integro-differential equation

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Abstract

In this paper, a numerical method is presented to solve a nonlinear weakly singular time-fractional partial integro–differential equation with Caputo fractional derivative. An orthogonal basis of spline space called O-spline is introduced, which is used for spatial approximations. Also, an approximation for the temporal Riemann–Liouville integral of the function is presented. A new parametric approximation is developed for the temporal Caputo fractional derivative of the function. Finally, using the weighted finite difference method, a numerical time scheme is obtained to approximate the equation. The convergence of this numerical scheme is investigated and some numerical examples are provided to illustrate the accuracy and efficiency of the method.

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Acknowledgements

We are very grateful to anonymous referees for their careful reading and valuable comments which led to the improvement of this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, 41938, Iran

    Javad Alavi & Hossein Aminikhah

  2. Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, P.O. Box 1914, Rasht, 41938, Iran

    Hossein Aminikhah

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  1. Javad Alavi
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  2. Hossein Aminikhah
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All authors contributed equally and significantly in writing this paper. All authors have read and approved the final paper.

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Correspondence to Hossein Aminikhah.

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Alavi, J., Aminikhah, H. An efficient parametric finite difference and orthogonal spline approximation for solving the weakly singular nonlinear time-fractional partial integro-differential equation. Comp. Appl. Math. 42, 350 (2023). https://doi.org/10.1007/s40314-023-02491-8

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  • DOI: https://doi.org/10.1007/s40314-023-02491-8

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