Half-explicit Runge-Kutta methods for semi-explicit differential- algebraic equations of index 1
type: Item
instance of: scholarly article
title: Half-explicit Runge-Kutta methods for semi-explicit differential- algebraic equations of index 1
zbMATH Open document ID: 0791.65055
DOI: 10.1007/BF01388697
author: Martin Arnold
author: R. Weiner
author: K. Strehmel
published in: Numerische Mathematik
publication date: 1994-07-07T00:00:00Z
full work available at URL: https://eudml.org/doc/133713
review text: For the numerical solution of non-stiff semi-explicit differential- algebraic equations (DAEs) of index 1 half-explicit Runge-Kutta methods (HERK) are considered that combine an explicit Runge-Kutta method for the differential part with a simplified Newton method for the (approximate) solution of the algebraic part of the DAE. Two principles for the choice of the initial guesses and the number of Newton steps at each stage are given that allow to construct HERK of the same order as the underlying explicit Runge-Kutta method. Numerical tests illustrate the efficiency of these methods.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 569107
zbMATH Keywords: non-stiff semi-explicit differential-algebraic equations of index 1
zbMATH Keywords: half-explicit Runge-Kutta methods
zbMATH Keywords: numerical tests
zbMATH Keywords: Newton method
MaRDI profile type: Publication
cites work: Q4002188
cites work: Q4725642
cites work: One-step and extrapolation methods for differential-algebraic systems
cites work: A family of embedded Runge-Kutta formulae
cites work: Q3766743
cites work: ODE Methods for the Solution of Differential/Algebraic Systems
cites work: Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
cites work: Solving Ordinary Differential Equations I
cites work: On the Butcher group and general multi-value methods
cites work: Q4000061
cites work: High order embedded Runge-Kutta formulae
cites work: Order Results for Implicit Runge–Kutta Methods Applied to Differential/Algebraic Systems
cites work: The application of Rosenbrock-Wanner type methods with stepsize control in differential-algebraic equations
cites work: Rosenbrock methods for differential algebraic equations
cites work: On error behaviour of partitioned linearly implicit Runge-Kutta methods for stiff and differential algebraic systems
OpenAlex ID: W2033720550
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description: scientific article; zbMATH DE number 569107