Event location for ordinary differential equations (Q1570154)

Given an initial value problem (IVP) \(y'= f(t,y)\), an event is said to occur at \(t^*\) when \(g(t^*,y(t^*))= 0\). This paper considers problems for which the IVP changes at the time of an event. It is shown that under the assumption that a solver produces a piecewise polynomial solution which is uniformly accurate to a certain order then this same order is achieved in the presence of isolated events. Numerical results confirm this behaviour. In addition some discussion is given on how a solver ``notices'' an event.