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Volume 42, Issue 2
Generalized Jacobi Spectral Galerkin Method for Fractional-Order Volterra Integro-Differential Equations with Weakly Singular Kernels

Yanping Chen, Zhenrong Chen & Yunqing Huang

DOI: 10.4208/jcm.2209-m2022-0129

J. Comp. Math., 42 (2024), pp. 355-371.

Published online: 2024-01

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65L05, 65L20, 65L50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-355, author = {Chen , YanpingChen , Zhenrong and Huang , Yunqing}, title = {Generalized Jacobi Spectral Galerkin Method for Fractional-Order Volterra Integro-Differential Equations with Weakly Singular Kernels}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {2}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2209-m2022-0129}, url = {http://global-sci.org/intro/article_detail/jcm/22884.html} }
TY - JOUR T1 - Generalized Jacobi Spectral Galerkin Method for Fractional-Order Volterra Integro-Differential Equations with Weakly Singular Kernels AU - Chen , Yanping AU - Chen , Zhenrong AU - Huang , Yunqing JO - Journal of Computational Mathematics VL - 2 SP - 355 EP - 371 PY - 2024 DA - 2024/01 SN - 42 DO - http://doi.org/10.4208/jcm.2209-m2022-0129 UR - https://global-sci.org/intro/article_detail/jcm/22884.html KW - Generalized Jacobi spectral Galerkin method, Fractional-order Volterra integro-differential equations, Weakly singular kernels, Convergence analysis. AB -

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.

Chen , YanpingChen , Zhenrong and Huang , Yunqing. (2024). Generalized Jacobi Spectral Galerkin Method for Fractional-Order Volterra Integro-Differential Equations with Weakly Singular Kernels. Journal of Computational Mathematics. 42 (2). 355-371. doi:10.4208/jcm.2209-m2022-0129
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