Error Analysis of Fractional Collocation Methods for Volterra Integro-Differential Equations with Noncompact Operators
Year: 2025
Author: Zheng Ma, Chengming Huang, Anatoly A. Alikhanov
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 690–707
Abstract
This paper is concerned with the numerical solution of Volterra integro-differential equations with noncompact operators. The focus is on the problems with weakly singular solutions. To handle the initial weak singularity of the solution, a fractional collocation method is applied. A rigorous $hp$-version error analysis of the numerical method under a weighted $H^1$-norm is carried out. The result shows that the method can achieve high order convergence for such equations. Numerical experiments are also presented to confirm the effectiveness 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.2401-m2023-0196
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 690–707
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Volterra integro-differential equation Noncompact operator Nonsmooth solution Collocation method Fractional polynomial $hp$-version error analysis.