GAUTSCHI-TYPE AND IMPLICIT-EXPLICIT INTEGRATORS FOR CONSTRAINED WAVE EQUATIONS

Altmann, R.

doi:10.1090/mcom/4194

GAUTSCHI-TYPE AND IMPLICIT-EXPLICIT INTEGRATORS FOR CONSTRAINED WAVE EQUATIONS

2026-03-01

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DOI：10.1090/mcom/4194

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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.

Keywords:

PDAE

Gautschi-type integrator

implicit-explicit Crank-Nicolson scheme

time discretization

GAUTSCHI-TYPE AND IMPLICIT-EXPLICIT INTEGRATORS FOR CONSTRAINED WAVE EQUATIONS

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