Numerical Solution to the System of Integro-Differential Equations Using Collocation Approximation

Abstract

The system of integro-differential equations (IDEs) has been utilized to model a wide range of problems in finance, control systems, viscoelasticity, engineering, and the wide-ranging applications of these equations in various fields of science. In this paper, we present efficient solvers for solving a system of high-order linear Volterra–Fredholm integro-differential equations (VFIDEs) using numerical techniques. The system of integro-differential equations is reduced to equations into a system of linear algebraic equations, and matrix inversion is employed to solve the algebraic equations. Only a small number of S-polynomials are needed to obtain a satisfactory result. The method’s error analysis is presented. Several examples are provided to demonstrate the use of the collocation approach. The numerical simulation demonstrates the dependability and efficiency of the collocation method. The proposed method is highly effective, straightforward, and well-suited for solving systems of Volterra integro-differential equations.