Time Discretization Schemes for Hyperbolic Systems on Networks by ε-Expansion

Abstract

We consider partial differential equations on networks with a small parameter ϵ, which are hyperbolic for ϵ>0 and parabolic for ϵ=0. With a combination of an ϵ-expansion and Runge-Kutta schemes for constrained systems of parabolic type, we derive a new class of time discretization schemes for hyperbolic systems on networks, which are constrained due to interconnection conditions. For the analysis we consider the coupled system equations as partial differential-algebraic equations based on the variational formulation of the problem. We discuss well-posedness of the resulting systems and estimate the error caused by the ϵ-expansion.