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Time-transformations for the event location in discontinuous ODEs

Authors: L. Lopez and S. Maset
Journal: Math. Comp.
MSC (2010): Primary 65L05
Published electronically: December 26, 2017
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Abstract: In this paper, we consider numerical methods for the location of events of ordinary differential equations. These methods are based on particular changes of the independent variable, called time-transformations. Such a time-transformation reduces the integration of an equation up to the unknown point, where an event occurs, to the integration of another equation up to a known point. This known point corresponds to the unknown point by means of the time-transformation. This approach extends the one proposed by Dieci and Lopez [BIT 55 (2015), no. 4, 987-1003], but our generalization permits, amongst other things, to deal with situations where the solution approaches the event in a tangential way. Moreover, we also propose to use this approach in a different manner with respect to that of Dieci and Lopez.

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Additional Information

L. Lopez
Affiliation: Dipartimento di Matematica, Università di Bari, 70126 Bari, Italy

S. Maset
Affiliation: Dipartimento di Matematica e Geoscienze, Università di Trieste, 34127 Trieste, Italy

Received by editor(s): March 25, 2016
Received by editor(s) in revised form: March 24, 2017
Published electronically: December 26, 2017
Additional Notes: This paper was supported in part by the GNCS of the Italian “Istituto Nazionale di Alta Matematica”.
Article copyright: © Copyright 2017 American Mathematical Society

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