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June  2009, 11(4): 1057-1070. doi: 10.3934/dcdsb.2009.11.1057

Error analysis of stabilized semi-implicit method of Allen-Cahn equation

Xiaofeng Yang 1,

1. 

Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States

Received  July 2008 Revised  October 2008 Published  April 2009

We consider in this paper the stabilized semi-implicit (in time) scheme and the splitting scheme for the Allen-Cahn equation $\phi_t-\Delta\phi+$ε$^-2f(\phi)=0$ arising from phase transitions in material science. For the stabilized first-order scheme, we show that it is unconditionally stable and the error bound depends on ε-1 in some lower polynomial order using the spectrum estimate of [2, 10, 11]. In addition, the first- and second-order operator splitting schemes are proposed and the accuracy are tested and compared with the semi-implicit schemes numerically.
Keywords: Allen-Cahn equation, error analysis., semi-implicit methods.
Mathematics Subject Classification: Primary: 65M12, 76T99; Secondary: 65M7.
Citation: Xiaofeng Yang. Error analysis of stabilized semi-implicit method of Allen-Cahn equation. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 1057-1070. doi: 10.3934/dcdsb.2009.11.1057
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