Reducing the collocation parameters for a class of weakly singular Volterra integral equations

In this paper, we claim that imposing some verifiable conditions on the collocation parameters in order to obtain high order numerical results for a class of weakly singular Volterra integral equations with noncompact kernels. Due to the increasingly ill-conditioned linear systems which obtain through the standard collocation method with graded meshes, we will show that the associated linear systems are well-conditioned and a superconvergence result is occurred. The strategy is also illustrated by a numerical test problem