Year: 2021
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Li, Dong, Quan, Chaoyu
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3181174286