A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel

Abstract

The purpose of this paper is to provide a Jacobi-collocation method for solving second kind Volterra integral equations with a smooth kernel. This method leads to a fully discrete integral operator. First, it is shown that the fully discrete integral operator is stable in both $L^{\infty }$ and weighted $L^2$ norms. Then, the proposed approach is proved to arrive at an optimal (the most possible) convergent order in both norms. One numerical example demonstrates the efficiency and accuracy of the proposed method.