非线性矩阵微分方程的多点边界值问题分析

IF 0.8 4区数学 Q2 MATHEMATICS Differential Equations Pub Date : 2024-02-26 DOI:10.1134/s0012266123120017

A. N. Bondarev, V. N. Laptinskii

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引用次数: 0

摘要

摘要对于非线性微分矩阵方程，我们利用相应的基本矩阵对方程的线性部分进行正则化的构造方法，研究了多点边界值问题。根据问题的初始数据，我们获得了问题唯一可解性的充分条件。提出了包含相对简单计算过程的迭代算法来构建解。给出了迭代序列向解收敛的有效估计值，以及解定位域的估计值。

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Analysis of a Multipoint Boundary Value Problem for a Nonlinear Matrix Differential Equation

Abstract

For a nonlinear differential matrix equation, we study a multipoint boundary value problem by a constructive method of regularization over the linear part of the equation using the corresponding fundamental matrices. Based on the initial data of the problem, sufficient conditions for its unique solvability are obtained. Iterative algorithms containing relatively simple computational procedures are proposed for constructing a solution. Effective estimates are given that characterize the rate of convergence of the iteration sequence to the solution, as well as estimates of the solution localization domain.

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.