Stability of collocation methods for delay differential equations with vanishing delays

Hermann Brunner; Hui Liang

doi:10.1007/s10543-010-0285-1

Stability of collocation methods for delay differential equations with vanishing delays

Hermann Brunner^*
, Hui Liang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

21 Citations (Scopus)

Abstract

We analyze the asymptotic stability of collocation solutions in spaces of globally continuous piecewise polynomials on uniform meshes for linear delay differential equations with vanishing proportional delay qt (0<q<1) (pantograph DDEs). It is shown that if the collocation points are such that the analogous collocation solution for ODEs is A-stable, then this asymptotic behaviour is inherited by the collocation solution for the pantograph DDE.

Original language	English
Pages (from-to)	693-711
Number of pages	19
Journal	BIT Numerical Mathematics
Volume	50
Issue number	4
DOIs	https://doi.org/10.1007/s10543-010-0285-1
Publication status	Published - Dec 2010

User-Defined Keywords

Asymptotic stability on uniform meshes
Collocation methods
Delay differential equations
Implicit Runge-Kutta methods
Pantograph equation
Proportional vanishing delay

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10.1007/s10543-010-0285-1

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title = "Stability of collocation methods for delay differential equations with vanishing delays",

abstract = "We analyze the asymptotic stability of collocation solutions in spaces of globally continuous piecewise polynomials on uniform meshes for linear delay differential equations with vanishing proportional delay qt (0",

keywords = "Asymptotic stability on uniform meshes, Collocation methods, Delay differential equations, Implicit Runge-Kutta methods, Pantograph equation, Proportional vanishing delay",

author = "Hermann Brunner and Hui Liang",

note = "Funding Information: Acknowledgements The work of the first author has been supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant No. 9406) and by the Hong Kong Research Grants Council (RGC).",

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AU - Liang, Hui

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N2 - We analyze the asymptotic stability of collocation solutions in spaces of globally continuous piecewise polynomials on uniform meshes for linear delay differential equations with vanishing proportional delay qt (0

AB - We analyze the asymptotic stability of collocation solutions in spaces of globally continuous piecewise polynomials on uniform meshes for linear delay differential equations with vanishing proportional delay qt (0

KW - Asymptotic stability on uniform meshes

KW - Collocation methods

KW - Delay differential equations

KW - Implicit Runge-Kutta methods

KW - Pantograph equation

KW - Proportional vanishing delay

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DO - 10.1007/s10543-010-0285-1

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JF - BIT Numerical Mathematics

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Stability of collocation methods for delay differential equations with vanishing delays

Abstract

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