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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

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