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Effective time step analysis of convex splitting schemes for the Swift-Hohenberg equation

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Title
Effective time step analysis of convex splitting schemes for the Swift-Hohenberg equation
Author(s)
Seunggyu Lee; Yoon, Sungha; Kim, Junseok
Publication Date
2023-02
Journal
Journal of Computational and Applied Mathematics, v.419
Publisher
Elsevier BV
Abstract
We study the effective temporal step size of convex splitting schemes for the Swift- Hohenberg (SH) equation, which models the pattern formation in various physical systems. The convex splitting scheme is one of the most well-known numerical approaches with an unconditional stability for solving a gradient flow. Its stability, solvability, and convergence have been actively studied; however, only a few studies have analyzed the time step re-scaling phenomenon for certain applications. In this paper, we present effective time step formulations for different convex splitting methods. Several numerical simulations are conducted to confirm the effective time step analysis.(c) 2022 Elsevier B.V. All rights reserved.
URI
https://pr.ibs.re.kr/handle/8788114/13144
DOI
10.1016/j.cam.2022.114713
ISSN
0377-0427
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > 1. Journal Papers (저널논문)
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