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

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∞ and weighted L2 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.