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arXiv · 2107.07332

Negative time splitting is stable

Dong Li·Chaoyu Quan
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Abstract

For high order (than two) in time operator-splitting methods applied to dissipative systems, a folklore issue is the appearance of negative-time/backward-in-time linear evolution operators such as backward heat operators interwoven with nonlinear evolutions. The stability of such methods has remained an ensuing difficult open problem. In this work we consider a fourth order operator splitting discretization for the Allen-Cahn equation which is a prototypical high order splitting method with negative time-stepping, i.e. backward in time integration for the linear parabolic part. We introduce a new theoretical framework and prove uniform energy stability and higher Sobolev stability. This is the first strong stability result for negative time stepping operator-splitting methods.

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Dong Li, Chaoyu Quan. 2021-07-15. Negative time splitting is stable. https://arxiv.org/abs/2107.07332

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