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Computational study based on the Laplace transform and local discontinuous Galerkin methods for solving fourth-order time-fractional partial integro-differential equations with weakly singular kernels

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Abstract

The aim of this paper is to implement the high-order local discontinuous Galerkin method (LDGM) for solving partial integro-differential equations (PIDEs) in two dimensions. Time marching method and the transform-based method known as the non-time marching method can be used to discretize temporal terms. The combination of a small time step size in time marching methods and a high-order scheme in space with many degrees of freedom requires a considerable amount of computational time. In order to address this limitation, we propose an algorithm based on a combination of the Laplace transform and LDGM for solving fourth-order time-fractional (TF) PIDEs with weakly singular kernels. Unlike time-marching approaches, the transform-based method has a much lower computational complexity and can take advantage of parallel computing. A numerical experiment validates the accuracy and applicability of the proposed temporal discretization approach and also shows that k-degree LDG solutions have a \(k + 1\) convergence rate.

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Acknowledgements

We want to express our gratitude to the reviewers for their valuable suggestions and comments that helped to enhance the paper

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnique), No. 424, Hafez Ave., Tehran, 15914, Iran

    Hadi Mohammadi-Firouzjaei, Hojatollah Adibi & Mehdi Dehghan

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  1. Hadi Mohammadi-Firouzjaei
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  2. Hojatollah Adibi
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  3. Mehdi Dehghan
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Mohammadi-Firouzjaei, H., Adibi, H. & Dehghan, M. Computational study based on the Laplace transform and local discontinuous Galerkin methods for solving fourth-order time-fractional partial integro-differential equations with weakly singular kernels. Comp. Appl. Math. 43, 324 (2024). https://doi.org/10.1007/s40314-024-02813-4

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