Gautschi-type and implicit–explicit integrators for constrained wave equations

This paper deals with the construction and analysis of two integrators for (semi-linear) second-order partial differential–algebraic equations of semi-explicit type. More precisely, we consider an implicit–explicit Crank–Nicolson scheme as well as an exponential integrator of Gautschi type. For this, well-known wave integrators for unconstrained systems are combined with techniques known from the field of differential–algebraic equations. This results in efficient time stepping schemes that are provable of second order. Moreover, we discuss the practical implementation of the Gautschi-type method, which involves the solution of certain saddle point problems. The theoretical results are verified by a numerical experiment for the wave equation with kinetic boundary conditions.