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.