Error Analysis of Fractional Collocation Methods for Volterra Integro-Differential Equations with Noncompact Operators

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.