Multi-projection method for Volterra integral equations at the collocation points

This study tries to reach a new order of convergence at the collocation points. For this reason we estimated the solution of the Volterra integral equation to lower and upper solutions on the Sm−1(−1) whose elements are spline polynomials of degree m−1. Since the upper solution is based on the iterated method the superconvergence cannot be accrued at the collocation points. In fact, the upper solution at these points is equal to zero. Therefore, the lower solution which is obtained from the linear system of equations is supposed as an approximating solution at the collocation points and the order of convergence at these points for m=1 is 2 and otherwise m+2.