Solution of differential algebraic equations with the Fredholm operator by the least squares method

被引：7

作者：

Chistyakova, E. V. ^{[1
]}

Chistyakov, V. F. ^{[1
]}

机构：

[1] Russian Acad Sci, Siberian Branch, Inst Syst Dynam & Control Theory, Moscow, Russia

来源：

APPLIED NUMERICAL MATHEMATICS | 2020年 / 149卷

基金：

俄罗斯基础研究基金会;

关键词：

Differential algebraic equations; Index; Numerical schemes; Higher order; Fredholm equations; Volterra equations; Least squares method; INDEX;

D O I：

10.1016/j.apnum.2019.04.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper addresses systems of linear integral differential equations with a singular matrix multiplying the higher derivative of the desired vector-function. Such systems can be viewed as differential algebraic equations perturbed by the Fredholm operators. For such problems, we obtain solvability conditions and discuss the influence of small perturbations of the input data on the solution. Within the existence theorems, we propose the least squares method to obtain a numerical approximation. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：43 / 51

页数：9

共 50 条

[1] Solution of the Cauchy problem for two differential-algebraic equations with a Fredholm operator
Zubova, SP
DIFFERENTIAL EQUATIONS, 2005, 41 (10) : 1486 - 1489
[2] Solution of the Cauchy Problem for Two Differential-Algebraic Equations with a Fredholm Operator
S. P. Zubova
Differential Equations, 2005, 41 : 1486 - 1489
[3] Least squares approximation method for the solution of Volterra-Fredholm integral equations
Wang, Qisheng
Wang, Keyan
Chen, Shaojun
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 272 : 141 - 147
[4] Polynomial Least Squares Method for the Solution of Nonlinear Volterra-Fredholm Integral Equations
Caruntu, Bogdan
Bota, Constantin
MATHEMATICAL PROBLEMS IN ENGINEERING, 2014, 2014
[5] ON A LEAST-SQUARES COLLOCATION METHOD FOR LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS
HANKE, M
NUMERISCHE MATHEMATIK, 1988, 54 (01) : 79 - 90
[6] Application of the Least Squares Method to Solving Linear Differential-Algebraic Equations
Chistyakov, V. F.
Chistyakova, E. V.
NUMERICAL ANALYSIS AND APPLICATIONS, 2013, 6 (01) : 77 - 90
[7] The Polynomial Least Squares Method for Nonlinear Fractional Volterra and Fredholm Integro-Differential Equations
Caruntu, Bogdan
Pasca, Madalina Sofia
MATHEMATICS, 2021, 9 (18)
[8] ON THE APPROXIMATION TO SOLUTIONS OF OPERATOR EQUATIONS BY THE LEAST SQUARES METHOD
Gorbachuk, Myroslav L.
Gorbachuk, Valentyna I.
METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2008, 14 (03): : 229 - 241
[9] An algebraic least squares reduced basis method for the solution of nonaffinely parametrized Stokes equations
Dal Santo, N.
Deparis, S.
Manzoni, A.
Quarteroni, A.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2019, 344 : 186 - 208
[10] On the approximation to solutions of operator equations by the least squares method
M. L. Gorbachuk
Functional Analysis and Its Applications, 2005, 39 : 71 - 75

← 1 2 3 4 5 →