A three‐level linearized compact difference scheme for the Ginzburg–Landau equation |
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| Authors: | Zhao‐Peng Hao Zhi‐Zhong Sun Wan‐Rong Cao |
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| Affiliation: | Department of Mathematics, Southeast University, Nanjing, People's Republic of China |
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| Abstract: | ![]()
A high‐order finite difference method for the two‐dimensional complex Ginzburg–Landau equation is considered. It is proved that the proposed difference scheme is uniquely solvable and unconditionally convergent. The convergent order in maximum norm is two in temporal direction and four in spatial direction. In addition, an efficient alternating direction implicit scheme is proposed. Some numerical examples are given to confirm the theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 876–899, 2015 |
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| Keywords: | Ginzburg– Landau equation compact difference scheme convergence solvability |
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