8-Step Method for Third Order Fredholm Integro-Differential Equations with Vieta-Pell-Lucas as Approximating Function.

Abstract

Purpose: In this paper, we derive multistep numerical methods for third order linear Fredholm integro-differential equation using Vieta-Pell-Lucas polynomial as approximating function. Methodology: These new method is implemented by embedding it with Trapezoidal, Booles and Simpson 1/3 numerical methods. The derivation led to a block of twenty-four discrete schemes which simultaneously solves the third order linear integro-differential equation. The qualitative properties of the schemes have been investigated. Findings: The analysis of the method reveals that the proposed method is of order seven and the method is found to be consistent and stable, hence convergent. Unique contributor to theory, policy and practice: Numerical experiments have been performed on some selected problems and the results show that the proposed method perform creditably well when compared with the exact solution of the selected examples