Reliable solution of special event location problems for ODEs

Computing the solution of the initial value problem in ordinary differential equations (ODEs) may be only part of a larger task. One such task is finding where an algebraic function of the solution (an event function) has a root (an event occurs). This is a task which is difficult both in theory and in software practice. For certain useful kinds of event functions, it is possible to avoid two fundamental difficulties. It is described how to achieve the reliable solutions of such problems in a way that allows the capability to be grafted onto popular codes for the initial value problem.