Solving Volterra integral equations via fourth-degree hat functions

Abstract

The goal of this paper is to develop a novel operation matrix approach to solving Volterra integral equations by constructing fourth-degree hat functions and investigating their properties. This approach requires turning the problem under dissection into a set of algebraic equations and then solving it by any numerical method. In addition, we demonstrate that the convergence of this approach is of the order of O(h5), and numerical results show that it is practical and useful for dealing with such problems.