Time transformations for state-dependent delay differential equations

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January 2010, 9(1): 23-45. doi: 10.3934/cpaa.2010.9.23

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 August 2008 Revised June 2009 Published October 2009

Abstract
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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: changes of variable, breaking points, superconvergence, Delay differential equations, state-dependent delays.

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

Citation: Hermann Brunner, Stefano Maset. Time transformations for state-dependent delay differential equations. Communications on Pure & Applied Analysis, 2010, 9 (1) : 23-45. doi: 10.3934/cpaa.2010.9.23

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