Study of coupled integro-differential equations of Fredholm-Volterra with a nonlocal boundary value problem

This work investigates the nonlocal problems that arise from a coupled system of Fredholm-Volterra integro-differential equations with nonlocal boundary conditions. A theoretical investigation is conducted into the existence and uniqueness of the solution, as well as the continuous dependence of the coupled system on the given data. To validate the theoretical findings, illustrative examples are presented. Additionally, a numerical approach is employed, utilizing the trapezoidal rule and central difference schemes to transform the coupled system into an algebraic framework, which is then solved computationally to obtain approximate solutions. This system can be computationally solved to derive the approximate solution. There is also discussion of an error estimation. To illustrate the correctness of the techniques used, the numerical and exact solutions are finally compared, with graphical representations of the comparisons provided.