Abstract

The numerical solution of systems of linear ordinary differential equations with nonlocal nonlinear conditions depending on the values of the desired function at intermediate points is investigated. Conditions for the existence of a solution to the problem under consideration are given. For the numerical solution, an approach is proposed that reduces the problem to two auxiliary linear systems of differential equations with linear conditions and to a single nonlinear algebraic system with a dimension depending only on the number of given intermediate points. The proposed approach is illustrated by solving two problems. The auxiliary problems are solved analytically in one of them and numerically in the other.

中文翻译：

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具有非局部非线性条件的线性微分方程的数值解

摘要

研究了具有非局部非线性条件的线性常微分方程组的数值解，该解取决于期望函数在中间点的值。给出了所考虑问题的解决方案存在的条件。对于数值解，提出了一种将问题简化为两个具有线性条件的微分方程的辅助线性系统和一个仅取决于给定中间点数的单个非线性代数系统的方法。通过解决两个问题来说明所提出的方法。辅助问题在其中一个中通过解析来解决，而在另一个中通过数值来解决。