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.
| Original language | English |
|---|---|
| Article number | 114713 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 419 |
| DOIs | |
| Publication status | Published - 2023 Feb |
Bibliographical note
Funding Information:The first author (S. Lee) was supported by a Korea University Grant and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2020R1A2C1A01100114 ). The author (S. Yoon) was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT of Korea (MSIT) (No. 2019R1A6A1A11051177 ) and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2022R1I1A1A01073661 ). The corresponding author (J.S. Kim) was supported by Korea University Grant. The authors thank the reviewers for their valuable comments regarding the revision of this paper.
Publisher Copyright:
© 2022 Elsevier B.V.
Keywords
- Convex splitting scheme
- Effective time step
- Fourier analysis
- Swift–Hohenberg equation
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics