Rosenbrock methods for differential algebraic equations
type: Item
instance of: scholarly article
title: Rosenbrock methods for differential algebraic equations
zbMATH Open document ID: 0613.65076
DOI: 10.1007/BF01401021
author: Michel Roche
published in: Numerische Mathematik
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133224
review text: This paper deals with the numerical solution of differential algebraic equations (DAE) of index one. It begins with the development of a general theory on the Taylor expansion for the exact solutions of these problems, which extends the well known theory of Butcher for first order ordinary differential equations to DAE's of index one. As an application, we obtain Butcher-type results for Rosenbrock methods applied to DAE's of index one and we characterize numerical methods as applications of certain sets of trees. We derive convergent embedded methods of order 4(3) which require 4 or 5 evaluations of the functions, 1 evaluation of the Jacobian and 1 LU factorization per step.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 3992835
zbMATH Keywords: differential algebraic equations
zbMATH Keywords: index one
zbMATH Keywords: Taylor expansion
zbMATH Keywords: Rosenbrock methods
zbMATH Keywords: convergent embedded methods
describes a project that uses: DASSL
MaRDI profile type: Publication
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OpenAlex ID: W1991424184
description: scientific article; zbMATH DE number 3992835