Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 72, Issue 3, Pages 620-631Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2016.05.011
Keywords
Conservative Allen-Cahn equation; High-order method; Mass conservative method; Fourier spectral method
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Funding
- Basic Science Research Program through National Research Foundation of Korea (NRF) - Ministry of Education [2009-0093827]
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The conservative Allen-Cahn (AC) equation has been studied analytically and numerically. Our mathematical analysis and numerical experiment, however, show that previous numerical methods are not second-order accurate in time and/or do not conserve the initial mass. The aim of this paper is to propose high-order and mass conservative methods for solving the conservative AC equation. In the methods, we discretize the conservative AC equation by using a Fourier spectral method in space and first-, second-, and third-order implicit-explicit Runge-Kutta schemes in time. We show that the methods inherit the mass conservation, Numerical experiments are presented demonstrating the accuracy and efficiency of proposed methods. (C) 2016 Elsevier Ltd. All rights reserved.
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