Time Reparametrization and Event Location for Discontinuous Differential Algebraic Equations

Abstract

In this paper, we consider numerical methods for the event location of differential algebraic equations. The event corresponds to cross a discontinuity surface, beyond which another differential algebraic equation holds. The methods are based on a particular change of the independent variable time, called time reparametrization or time transformation, reducing the equation to another equation where the event time is known in advance. From a numerical point of view, these methods never cross the discontinuity surface and reach it in a fixed number of steps. The methods works also for differential algebraic equations of index higher than one.