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arXiv · 2004.13503

Operator splitting for abstract Cauchy problems with dynamical boundary condition

Petra Csomós·Matthias Ehrhardt·Bálint Farkas
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Abstract

In this work we study operator splitting methods for a certain class of coupled abstract Cauchy problems, where the coupling is such that one of the problems prescribes a "boundary type" extra condition for the other one. The theory of one-sided coupled operator matrices provides an excellent framework to study the well-posedness of such problems. We show that with this machinery even operator splitting methods can be treated conveniently and rather efficiently. We consider three specific examples: the Lie (sequential), the Strang and the weighted splitting, and prove the convergence of these methods along with error bounds under fairly general assumptions.

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Petra Csomós, Matthias Ehrhardt, Bálint Farkas. 2020-04-27. Operator splitting for abstract Cauchy problems with dynamical boundary condition. https://arxiv.org/abs/2004.13503

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