Error Analysis of Fractional Collocation Methods for Volterra Integro-Differential Equations with Noncompact Operators (Journal of Computational Mathematics, 2024)
This paper is concerned with the numerical solution of Volterra integro-differentialequations with noncompact operators. The focus is on the problems with weakly singularsolutions. To handle the initial weak singularity of the solution, a fractional collocationmethod is applied. A rigorous $hp$-version error analysis of the numerical method undera weighted $H^1$-norm is carried out. The result shows that the method can achieve highorder convergence for such equations. Numerical experiments are also presented to confirmthe effectiveness of the proposed method.