Unconditionally stable difference methods for delay partial differential equations
type: Item
instance of: scholarly article
title: Unconditionally stable difference methods for delay partial differential equations
zbMATH Open document ID: 1272.65066
author: Stefan Vandewalle
author: Chengming Huang
published in: Numerische Mathematik
publication date: 2013-02-04T00:00:00Z
full work available at URL: https://lirias.kuleuven.be/handle/123456789/302506
review text: The authors study finite difference approximations of parabolic partial differential equations with time-delay. They show that a variant of the classical second-order central difference approximation of the diffusion operator together with an approximation of the delay argument through linear interpolation and with the trapezoidal rule or with the second-order backward differentiation formula for the time derivative lead to a discretization which unconditionally preserves the delay dependent asymptotic stability of the linear test problem. Some numerical experiments illustrate the theoretical findings.
reviewed by: Iwan Gawriljuk
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35R10
zbMATH DE Number: 6134328
zbMATH Keywords: parabolic PDE with time-delay
zbMATH Keywords: difference methods on a non-constrained mesh
zbMATH Keywords: stability
zbMATH Keywords: backward differentiation formula
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
OpenAlex ID: W1963927951
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DOI: 10.1007/S00211-012-0467-7
description: scientific article; zbMATH DE number 6134328