Time transformations for state-dependent delay differential equations

Hermann BRUNNER; S. Maset

doi:10.3934/cpaa.2010.9.23

Time transformations for state-dependent delay differential equations

Hermann BRUNNER^*, S. Maset

^*Corresponding author for this work

Department of Mathematics

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

5 Citations (Scopus)

Abstract

In this paper we analyze particular changes of variable, called time transformations, reducing a delay differential equation with a state-dependent delay to a delay differential equation with a prescribed non-state-dependent delay. We then employ these transformations to compute the breaking points of solutions and to derive optimal superconvergence results for Runge-Kutta methods for state-dependent equations.

Original language	English
Pages (from-to)	23-45
Number of pages	23
Journal	Communications on Pure and Applied Analysis
Volume	9
Issue number	1
DOIs	https://doi.org/10.3934/cpaa.2010.9.23
Publication status	Published - Jan 2010

User-Defined Keywords

Breaking points
Changes of variable
Delay differential equations
State-dependent delays
Superconvergence

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10.3934/cpaa.2010.9.23

Cite this

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title = "Time transformations for state-dependent delay differential equations",

abstract = "In this paper we analyze particular changes of variable, called time transformations, reducing a delay differential equation with a state-dependent delay to a delay differential equation with a prescribed non-state-dependent delay. We then employ these transformations to compute the breaking points of solutions and to derive optimal superconvergence results for Runge-Kutta methods for state-dependent equations.",

keywords = "Breaking points, Changes of variable, Delay differential equations, State-dependent delays, Superconvergence",

author = "Hermann BRUNNER and S. Maset",

note = "The work of the first author has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant No. 9406). ",

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AU - Maset, S.

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PY - 2010/1

Y1 - 2010/1

N2 - In this paper we analyze particular changes of variable, called time transformations, reducing a delay differential equation with a state-dependent delay to a delay differential equation with a prescribed non-state-dependent delay. We then employ these transformations to compute the breaking points of solutions and to derive optimal superconvergence results for Runge-Kutta methods for state-dependent equations.

AB - In this paper we analyze particular changes of variable, called time transformations, reducing a delay differential equation with a state-dependent delay to a delay differential equation with a prescribed non-state-dependent delay. We then employ these transformations to compute the breaking points of solutions and to derive optimal superconvergence results for Runge-Kutta methods for state-dependent equations.

KW - Breaking points

KW - Changes of variable

KW - Delay differential equations

KW - State-dependent delays

KW - Superconvergence

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M3 - Journal article

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JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 1

ER -

Time transformations for state-dependent delay differential equations

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