Semi-explicit time-stepping methods for dynamical systems with complementarity constraints

In this paper we consider numerical methods for dynamical systems with complementary conditions. The dynamics of these systems are characterized by possible jumps in the solution caused by events which separate continuous phases of the state vector. These events occur on the basis of certain inequality constraints similar to those appearing in the context of dynamic optimization. The numerical techniques used up till now, were based on the implicit backward Euler method, while we explore one-step procedures based on semi-explicit schemes.