Continuous extensions of Rosenbrock-type methods
type: Item
instance of: scholarly article
title: Continuous extensions of Rosenbrock-type methods
zbMATH Open document ID: 0697.65055
DOI: 10.1007/BF02247965
published in: Computing
publication date: 1990-01-01T00:00:00Z
review text: Solving the initial value problem for ordinary differential equations by a one-step method gives, in general, only discrete approximations at the grid points. For various applications these discrete values are not sufficient. One should have instead a so-called dense output (continuous extension): a numerical solution defined for each x belonging to the interval of integration. This paper deals with the construction of continuous extensions for Rosenbrock methods. Existence theorems - with no extra states - are proved. The extension for differential-algebraic equations is also considered. A numerical example for differential-algebraic equations illustrates the relevancy of the theory for practical computation.
reviewed by: Z.Schneider
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4143366
zbMATH Keywords: one-step method
zbMATH Keywords: continuous extensions
zbMATH Keywords: Rosenbrock methods
zbMATH Keywords: differential- algebraic equations
zbMATH Keywords: numerical example
author: Alexander Ostermann
describes a project that uses: RODAS
MaRDI profile type: Publication
cites work: Stability Properties of Interpolants for Runge–Kutta Methods
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cites work: Practical Aspects of Interpolation in Runge-Kutta Codes
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cites work: A study of Rosenbrock-type methods of high order
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cites work: Rosenbrock methods for differential algebraic equations
cites work: An Attempt to Avoid Exact Jacobian and Nonlinear Equations in the Numerical Solution of Stiff Differential Equations
cites work: Natural Continuous Extensions of Runge-Kutta Methods
full work available at URL: https://doi.org/10.1007/bf02247965
OpenAlex ID: W1559157053
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description: scientific article; zbMATH DE number 4143366