Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential Equation

Abstract

In this paper, the existence and uniqueness of the Fredholm–Volterra integro-differential equation with the nonlocal condition will be studied. Also, we study the continuous dependence of the initial data. The numerical solution of the problem will be studied using the central difference approximations and trapezoidal rule to transform the Volterra–Fredholm integro-differential equation into a system of algebraic equations which can be solved together to get the solution. Finally, we solve some examples numerically to show the accuracy of the proposed method.