Higher-order additive Runge-Kutta schemes for ordinary differential equations
type: Item
instance of: scholarly article
title: Higher-order additive Runge-Kutta schemes for ordinary differential equations
zbMATH Open document ID: 1408.65045
author: Christopher A. Kennedy
author: Mark Carpenter
published in: Applied Numerical Mathematics
publication date: 2018-12-19T00:00:00Z
review text: The paper considers the numerical approximation of a system of ODEs where the right-hand side can be expressed as a sum of \(N\geq 2\) terms. The numerical scheme assumes a different integrator for each term. In particular, the authors develop two new additive Runge-Kutta (ARK\(_2\)) methods of order four and five, in an IMEX (implicit-explicit) formulation, for the case \(N=2\). The proposed numerical approach combines explicit Runge-Kutta (ERK) methods with explicit, singly-diagonally implicit (ESDIRK) methods, with error and step-size control implemented through a PID controller. The main features of the methods are discussed, especially those related to order conditions, error, linear stability and step-size control. The new methods are tested using two singular perturbation problems: Van der Pol equation and Kaps problem. The numerical tests indicate that the proposed methods present improvements in comparison to other existing methods of the same class.
reviewed by: Joseph Páez Chávez
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L04
Mathematics Subject Classification ID: 65L11
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 6995993
zbMATH Keywords: Runge-Kutta
zbMATH Keywords: L-stability
zbMATH Keywords: stiff ODE
zbMATH Keywords: singularly perturbed problem
zbMATH Keywords: IMEX
describes a project that uses: Mathematica
describes a project that uses: RODAS
describes a project that uses: PIROCK
describes a project that uses: STDTST
describes a project that uses: NSDTST
MaRDI profile type: Publication
full work available at URL: j.apnum.2018.10.007
OpenAlex ID: W2899139000
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Higher-order additive Runge-Kutta schemes for ordinary differential equations (Wikidata QID)
Wikidata QID: Q128977846

Higher-order additive Runge-Kutta schemes for ordinary differential equations (DOI)
DOI: 10.1016/J.APNUM.2018.10.007

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