‎An effective computational approach based on‎ ‎new multi-step collocation method for solving integral-algebraic equations‎

Abstract

‎Some efficient numerical schemes have been used to solve integral algebraic equations (IAEs)‎. ‎In this article‎, ‎in order to find higher order method with an extensive accuracy‎, ‎new multi-step collocation method is developed for the numerical solution of IAEs‎. ‎The convergence of the proposed method is investigated and convergence orders are determined‎. ‎Two examples have been thoroughly examined to validate theoretical advancements in practical application‎. ‎Also‎, ‎we apply one-step and multi-step collocation methods to solve IAEs and compare numerical results to‎ ‎show the efficiency and high accuracy of the proposed method‎. AMS subject classifications: 65R20, 45F15.