Novel approach for solving multipoint boundary value problem for integro-differential equation
arXiv:2309.15805
The paper investigates multipoint boundary value problems for systems of Fredholm integro‑differential equations, derives well‑posedness conditions, and proposes algorithms for approximate and numerical solutions, especially when the kernel is degenerate.
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.