On solving systems of differential algebraic equations
type: Item
instance of: scholarly article
title: On solving systems of differential algebraic equations
zbMATH Open document ID: 0764.65038
author: Marian Kwapisz
published in: Applications of Mathematics
publication date: 1993-05-16T00:00:00Z
full work available at URL: https://eudml.org/doc/15714
review text: A system of differential algebraic equations \(x'=f(t,x,y)\), \(y=g(t,x,y)\), \(x(0)=0\) is studied under the validity of many assumptions, e.g. \(f\), \(g\) fulfill local Lipschitz conditions. The convergence of successive approximations \(x_{k+1}(t)=\int_ 0^ t f(s,x_ k(s),y_ k(s))ds\), \(y_{k+1}=g(t,\bar x,\bar y))\), \(x_ 0\), \(y_ 0\) arbitrary, is proved where either \(\bar x=x_ k(t)\), \(\bar y=y_ k(t)\) (Picard method) or \(\bar x=x_{k+1}(t)\), \(\bar y=y_ k(t)\) (Seidel method).
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 165639
zbMATH Keywords: Picard method
zbMATH Keywords: Seidel method
zbMATH Keywords: system of differential algebraic equations
zbMATH Keywords: convergence
zbMATH Keywords: successive approximations
reviewed by: Miroslav Bartušek
MaRDI profile type: Publication
cites work: Q4767821
cites work: Q3976899
cites work: On the approximate solutions of an abstract equation
cites work: On the convergence of approximate iterations for an abstract equation
cites work: Q4146083
cites work: Q3702039
cites work: Q3797753
cites work: Q5652137
Recommended article: Q4898769
Recommended article: Q5459342
Recommended article: Algebraic solutions of algebraic differential equations
Recommended article: Q4827115
Recommended article: Q4722390
Recommended article: Solving systems differential-algebraic equations of high indices
Recommended article: Q4355387
Recommended article: Q4377056
Recommended article: On numerical solution of differential algebraic equations
Recommended article: Solutions of Linear Differential Algebraic Equations
description: scientific article; zbMATH DE number 165639