Novel approach for solving multipoint boundary value problem for integro-differential equation

TL;DR

This paper introduces a new method for solving multipoint boundary value problems for systems of Fredholm integro-differential equations, including degenerate kernel cases, with algorithms for approximate and numerical solutions.

Contribution

It develops well-posedness conditions and algorithms for solving multipoint boundary value problems for Fredholm integro-differential systems, especially with degenerate kernels.

Findings

Established conditions for well-posedness.

Developed algorithms for approximate solutions.

Addressed degenerate kernel cases separately.

Abstract

In the present paper, we study a multipoint boundary value problem for a system of Fredholm integro-differenial equations by the method of parameterization. The case of a degenerate kernel is studied separately, for which we obtain well-posedness conditions and propose some algorithms to find approximate and numerical solutions to the problem. Then we establish necessary and sufficient conditions for the well-posedness of the multipoint problem for the system of Fredholm integro-differential equations and develop some algorithms for finding its approximate solutions. These algorithms are based on the solutions of an approximating problem for the system of integro-differential equations with degenerate kernel.