Generalized Jacobi Spectral Galerkin Method for Fractional-Order Volterra Integro-Differential Equations with Weakly Singular Kernels

Generalized Jacobi Spectral Galerkin Method for Fractional-Order Volterra Integro-Differential Equations with Weakly Singular Kernels

Year:    2024

Author:    Yanping Chen, Zhenrong Chen, Yunqing Huang

Journal of Computational Mathematics, Vol. 42 (2024), Iss. 2 : pp. 355–371

Abstract

For fractional Volterra integro-differential equations (FVIDEs) with weakly singular kernels, this paper proposes a generalized Jacobi spectral Galerkin method. The basis functions for the provided method are selected generalized Jacobi functions (GJFs), which can be utilized as natural basis functions of spectral methods for weakly singular FVIDEs when appropriately constructed. The developed method’s spectral rate of convergence is determined using the $L^∞$-norm and the weighted $L^2$-norm. Numerical results indicate the usefulness of the proposed method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2209-m2022-0129

Journal of Computational Mathematics, Vol. 42 (2024), Iss. 2 : pp. 355–371

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Generalized Jacobi spectral Galerkin method Fractional-order Volterra integro-differential equations Weakly singular kernels Convergence analysis.

Author Details

Yanping Chen

Zhenrong Chen

Yunqing Huang

  1. A block-by-block strategy for fractional systems of nonlinear weakly singular integro-differential equations

    Afiatdoust, F.

    Heydari, M. H.

    Hosseini, M. M.

    Computational and Applied Mathematics, Vol. 42 (2023), Iss. 6

    https://doi.org/10.1007/s40314-023-02380-0 [Citations: 1]