Journal
INVERSE PROBLEMS AND IMAGING
Volume 7, Issue 3, Pages 679-695Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/ipi.2013.7.679
Keywords
Implicit-explicit scheme; Allen-Cahn equation; energy stability
Categories
Funding
- NSF of China [11271313]
- Hong Kong Scholars Program
- Hunan University
- Hong Kong Baptist University's Institute of Computational and Theoretical Studies
- Hong Kong Research Grant Council
- Hong Kong Baptist University
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In this paper, we will investigate the first- and second-order implicit-explicit schemes with parameters for solving the Allen-Cahn equation. It is known that the Allen-Cahn equation satisfies a nonlinear stability property, i.e., the free-energy functional decreases in time. The goal of this paper is to consider implicit-explicit schemes that inherit the nonlinear stability of the continuous model, which will be achieved by properly choosing parameters associated with the implicit-explicit schemes. Theoretical justifications for the nonlinear stability of the schemes will be provided, and the theoretical results will be verified by several numerical examples.
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