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

被引：0

作者：

Bulatov, Mikhail ^{[1
,2
]}

Indutskaya, Tatiana ^{[1
]}

Solovarova, Liubov ^{[1
]}

机构：

[1] Russian Acad Sci, Inst Syst Dynam & Control Theory, Siberian Branch, 134 Lermontov St, Irkutsk 664033, Irkutsk Region, Russia

[2] Buryat State Univ, 24A Smolin St, Ulan Ude 670000, Republic Of Bur, Russia

来源：

APPLIED NUMERICAL MATHEMATICS | 2025年 / 208卷

关键词：

Systems of nonlinear integral equations; Volterra; Integral-algebraic equations; Matrix pencils; Linearization; Quadrature formulas;

D O I：

10.1016/j.apnum.2024.10.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 illposedness. 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.

引用

页码：348 / 355

页数：8

共 20 条

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