Parallel two-step ROW-methods for stiff delay differential equations
type: Item
instance of: scholarly article
title: Parallel two-step ROW-methods for stiff delay differential equations
zbMATH Open document ID: 1172.65042
author: Qiao Zhu
author: Aiguo Xiao
published in: Applied Numerical Mathematics
publication date: 2009-07-02T00:00:00Z
review text: The authors investigate the GP-stability and GPL-stability of numerical methods for delay differential equations, \[ \left\{ \begin{matrix} y'(x)&=& f(x,y(x),y(x-\tau)), \quad x\geq 0\\ y(x)&=&g(x), \quad -\tau \leq x \leq 0. \end{matrix} \right. \] It is proved that a given parallel two-step ROW-method (PTSROW method) obtained by a Hout's interpolation technique from a method in the class of linearly-implicit methods obtained by \textit{H. Podhaisky, B. A. Schmitt} and \textit{R. Weiner} [Appl. Numer. Math. 42, No. 1--3, 381--395 (2002; Zbl 1005.65073)] is GP-stable or GPL-stable only if the one on the class is A-stable or L-stable respectively. Also, by means of tree theory and B-series the order of consistency conditions and the order of stage-order conditions for the PTSROW method is analyzed. The paper ends with the construction of two classes of stiffly-accurate PTSROW methods, also of two classes of real-time PTSROW methods, and with some numerical experiments implemented in parallel MPI C language to test accuracy and speed of sequential versus parallel implementation. The first example considers a stiff nonlinear ordinary differential equation, while the second is applied to a stiff linear delay differential equation.
reviewed by: Josep J. Masdemont
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 5574497
zbMATH Keywords: stiff delay differential equations
zbMATH Keywords: parallel two-step ROW-methods
zbMATH Keywords: GP- and GPL-stability
describes a project that uses: RODAS
MaRDI profile type: Publication
full work available at URL: j.apnum.2009.01.005
OpenAlex ID: W2007920546
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DOI: 10.1016/J.APNUM.2009.01.005
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description: scientific article; zbMATH DE number 5574497