Numerical Solution of Linear Volterra-Fredholm Integro-Differential Equations Using Lagrange Polynomials

Abstract

In this paper, we introduce a numerical method for solving linear Volterra-Fredholm integro-differential Equations (LVFIDE’s) of the first order. To solve these equations, we consider the polynomial approximation from original Lagrange polynomial approximation, barycentric Lagrange polynomial approximation, and modified Lagrange polynomial approximation. Finally, some examples are included to improve the validity and applicability of the techniques.

Keywords: Linear Volterra-Fredholm integro-differential equation, Original Lagrange polynomial, Barycentric Lagrange Polynomial, Modified Lagrange polynomial.