Time transformations for state-dependent delay differential equations

Hermann Brunner; Stefano Maset

doi:10.3934/cpaa.2010.9.23

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2010, Volume 9, Issue 1: 23-45. Doi: 10.3934/cpaa.2010.9.23

This issue Previous Article Time-frequency analysis of fourier integral operators Next Article Solutions with large total variation to nonconservative hyperbolic systems

Time transformations for state-dependent delay differential equations

Hermann Brunner^1, and
Stefano Maset^2,

1.
Dept. of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada A1C 5S7
2.
Dipartimento di Matematica e Informatica, Università di Trieste, I-34100 Trieste

Received: July 31, 2008

Revised: May 31, 2009

Published: December 2009

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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.

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Mathematics Subject Classification: 34K17, 34K28, 34K20.

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