拟线性积分代数方程数值解的一种算法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI:10.1016/j.apnum.2024.10.008

Mikhail Bulatov , Tatiana Indutskaya , Liubov Solovarova

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引用次数: 0

摘要

本文讨论了第一类和第二类相互关联的积分非线性Volterra方程。将它们结合起来，我们得到了一个同退化矩阵乘上主部分的积分方程组，通常称为积分代数方程。我们强调正在审议的问题的基本特征，即它们的不稳定性。给出了矩阵铅笔的唯一充分光滑解的存在条件，并基于最简单的正交公式和非线性被积函数的线性化，给出了其数值解的一种算法。给出了实例的说明和数值计算结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On an algorithm for the numerical solution of quasilinear integral-algebraic equations

This article addresses interrelated integral nonlinear Volterra equations of the first and second kinds. Combining them, we obtain a system of integral equations with an identically degenerate matrix multiplying by the main part, which is usually called integral-algebraic equations. We highlight the fundamental features of the problems under consideration, namely their ill-posedness. We give conditions for the existence of a unique sufficiently smooth solution in terms of matrix pencils and propose an algorithm for their numerical solution, which is based on the simplest quadrature formula and linearization of a nonlinear integrand. Illustrative examples and results of numerical calculations of test examples are given.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.