Dense output for extrapolation methods
type: Item
instance of: scholarly article
title: Dense output for extrapolation methods
zbMATH Open document ID: 0693.65048
DOI: 10.1007/BF01385634
published in: Numerische Mathematik
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133510
review text: This paper is concerned with dense output formulas for extrapolation methods for ordinary differential equations. In particular, the extrapolated explicit Euler method, the GBS method (for non-stiff equations) and the extrapolated linearly implicit Euler method (for stiff and differential-algebraic equations) are considered. Existence and uniqueness questions for dense output formulas are discussed and an algorithmic description for their construction is given. Several numerical experiments illustrate the theoretical results.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4135326
zbMATH Keywords: interpolants
zbMATH Keywords: stiff equations
zbMATH Keywords: dense output formulas
zbMATH Keywords: extrapolation methods
zbMATH Keywords: explicit Euler method
zbMATH Keywords: GBS method
zbMATH Keywords: non-stiff equations
zbMATH Keywords: implicit Euler method
zbMATH Keywords: differential-algebraic equations
zbMATH Keywords: numerical experiments
author: Ernst Hairer
author: Alexander Ostermann
reviewed by: Ernst Hairer
describes a project that uses: RODAS
MaRDI profile type: Publication
cites work: Asymptotic Error Expansions for Stiff Equations: The Implicit Euler Scheme
cites work: A semi-implicit mid-point rule for stiff systems of ordinary differential equations
cites work: A fifth-order interpolant for the Dormand and Prince Runge-Kutta method
cites work: Recent Progress in Extrapolation Methods for Ordinary Differential Equations
cites work: One-step and extrapolation methods for differential-algebraic systems
cites work: Q4727324
cites work: Interpolants for Runge-Kutta formulas
cites work: Effective solution of discontinuous IVPs using a Runge-Kutta formula pair with interpolants
cites work: Practical Aspects of Interpolation in Runge-Kutta Codes
cites work: On the stability of semi-implicit methods for ordinary differential equations
cites work: Q3831977
cites work: Extrapolation at stiff differential equations
cites work: The numerical solution of differential-algebraic systems by Runge-Kutta methods
cites work: Q3779682
cites work: Q4036825
cites work: Q4714145
cites work: Fourth- and Fifth-Order, Scaled Rungs–Kutta Algorithms for Treating Dense Output
cites work: A Simple Interpolation Algorithm for Improvement of the Numerical Solution of a Differential Equation
cites work: Continuous extensions of Rosenbrock-type methods
cites work: Order Barriers for Continuous Explicit Runge-Kutta Methods
cites work: Rosenbrock methods for differential algebraic equations
cites work: Interpolation for Runge–Kutta Methods
cites work: Output in extrapolation codes
cites work: Reliable solution of special event location problems for ODEs
cites work: Q3857636
cites work: Natural Continuous Extensions of Runge-Kutta Methods
OpenAlex ID: W2021362155
description: scientific article; zbMATH DE number 4135326