Time-transformations for the event location in discontinuous ODEs

Lopez, L.; Maset, S.

doi:10.1090/mcom/3305

Time-transformations for the event location in discontinuous ODEs
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by L. Lopez and S. Maset PDF

Math. Comp. 87 (2018), 2321-2341 Request permission

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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