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

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  19 September 2016

Zhengru Zhang  and
Yuanzi Ma
Zhengru Zhang*
Affiliation:
Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, 19 Xinjiekouwai Street, Haidian District, Beijing 100875, China
Yuanzi Ma*
Affiliation:
College of Science, China University of Petroleum–Beijing, 18 Fuxue Road, Changping, Beijing 102249, China
*
*Corresponding author. Email:[email protected] (Z. R. Zhang), [email protected] (Y. Z. Ma)
*Corresponding author. Email:[email protected] (Z. R. Zhang), [email protected] (Y. Z. Ma)
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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 schemes 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 methodenergy stableSwift-Hohenberg equationfinite difference method

MSC classification

Secondary: 65M06: Finite difference methods 65Z05: Applications to physics
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 6 , December 2016 , pp. 992 - 1003
Copyright
Copyright © Global-Science Press 2016 

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