Fast and accurate solvers for weakly singular Volterra integral equations in weighted spaces

For the numerical solution of Volterra integral equations of the second kind whose integrands have diagonal and endpoint algebraic singularities, we investigate in this paper, a fast modified collocation method based on the zeros of the Jacobi polynomials in appropriate weighted spaces. The iterated version of the standard collocation method is also defined. The proposed methods are shown to converge faster than the collocation scheme, and the Sloan iteration can be applied to the modified collocation solution to make it even more accurate. This research seems to be the first to explore superconvergent approaches for solving integral equations of this type. Some numerical tests are presented to show the effectiveness of the suggested methods.(c) 2023 Elsevier B.V. All rights reserved.