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 - <p style="text-align: justify;">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.</p>