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On a Large Time-Stepping Method for the Swift-Hohenberg Equation

On a Large Time-Stepping Method for the Swift-Hohenberg Equation
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Year:    2016

Author:    Zhengru Zhang, Yuanzi Ma

Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 6 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2014.m48

Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 6 : pp. 992–1003

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

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

Author Details

Zhengru Zhang

Yuanzi Ma

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  6. Bifurcation Analysis and Pattern Selection of Solutions for the Modified Swift–Hohenberg Equation

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  11. An energy-stable second-order finite element method for the Swift–Hohenberg equation

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