Volume 8, Issue 6
On a Large Time-Stepping Method for the Swift-Hohenberg Equation

Zhengru Zhang & Yuanzi Ma

Adv. Appl. Math. Mech., 8 (2016), pp. 992-1003.

Published online: 2018-05

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  • Abstract

The main purpose of this work is to contrast and analyze a large time-stepping numerical method for the Swift-Hohenberg (SH) equation. This model requires very large time simulation to reach steady state, so developing a large time step algorithm becomes necessary to improve the computational efficiency. In this paper, a semi-implicit Euler scheme in time is adopted. An extra artificial term is added to the discretized system in order to preserve the energy stability unconditionally. The stability property is proved rigorously based on an energy approach. Numerical experiments are used to demonstrate the effectiveness of the large time-stepping approaches by comparing with the classical scheme.

  • Keywords

Large time-stepping method, energy stable, Swift-Hohenberg equation, finite difference method.

  • AMS Subject Headings

65M06, 65Z05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-992, author = {Zhengru Zhang , and Ma , Yuanzi}, title = {On a Large Time-Stepping Method for the Swift-Hohenberg Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {6}, pages = {992--1003}, abstract = {

The main purpose of this work is to contrast and analyze a large time-stepping numerical method for the Swift-Hohenberg (SH) equation. This model requires very large time simulation to reach steady state, so developing a large time step algorithm becomes necessary to improve the computational efficiency. In this paper, a semi-implicit Euler scheme in time is adopted. An extra artificial term is added to the discretized system in order to preserve the energy stability unconditionally. The stability property is proved rigorously based on an energy approach. Numerical experiments are used to demonstrate the effectiveness of the large time-stepping approaches by comparing with the classical scheme.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m48}, url = {http://global-sci.org/intro/article_detail/aamm/12127.html} }
TY - JOUR T1 - On a Large Time-Stepping Method for the Swift-Hohenberg Equation AU - Zhengru Zhang , AU - Ma , Yuanzi JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 992 EP - 1003 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m48 UR - https://global-sci.org/intro/article_detail/aamm/12127.html KW - Large time-stepping method, energy stable, Swift-Hohenberg equation, finite difference method. AB -

The main purpose of this work is to contrast and analyze a large time-stepping numerical method for the Swift-Hohenberg (SH) equation. This model requires very large time simulation to reach steady state, so developing a large time step algorithm becomes necessary to improve the computational efficiency. In this paper, a semi-implicit Euler scheme in time is adopted. An extra artificial term is added to the discretized system in order to preserve the energy stability unconditionally. The stability property is proved rigorously based on an energy approach. Numerical experiments are used to demonstrate the effectiveness of the large time-stepping approaches by comparing with the classical scheme.

Zhengru Zhang & Yuanzi Ma. (2020). On a Large Time-Stepping Method for the Swift-Hohenberg Equation. Advances in Applied Mathematics and Mechanics. 8 (6). 992-1003. doi:10.4208/aamm.2014.m48
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