Numerical Solutions of Volterra Integral Equations with Subdivision-Based Collocation Approach

Abstract

Integral equations play a vital role in the fields of applied and computational mathematics. This paper introduces a unique subdivision-based collocation technique for solving the initial value problems (IVPs) arising from Volterra integral equations (VIEs). A suitable subdivision scheme is employed to develop the numerical algorithm for solving the VIEs. Several numerical illustrations are tested and compared with the existing methods for assessing the efficiency of the proposed numerical algorithm and error estimation.