Generalized Jacobi Spectral Galerkin Method for Fractional-Order Volterra Integro-Differential Equations with Weakly Singular Kernels (Journal of Computational Mathematics, 2024)
For fractional Volterra integro-differential equations (FVIDEs) with weakly singularkernels, this paper proposes a generalized Jacobi spectral Galerkin method. The basisfunctions for the provided method are selected generalized Jacobi functions (GJFs), whichcan be utilized as natural basis functions of spectral methods for weakly singular FVIDEswhen appropriately constructed. The developed method’s spectral rate of convergence isdetermined using the $L^∞$-norm and the weighted $L^2$-norm. Numerical results indicate theusefulness of the proposed method.
Keywords: Generalized Jacobi spectral Galerkin method; Fractional-order Volterra integro-differential equations; Weakly singular kernels; Convergence analysis.