Analysis of some finite difference schemes for two‐dimensional Ginzburg‐Landau equation |
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| Authors: | Tingchun Wang Boling Guo |
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| Institution: | Institute of Applied Physics and Computational Mathematics, Beijing 100088, China |
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| Abstract: | We study the rate of convergence of some finite difference schemes to solve the two‐dimensional Ginzburg‐Landau equation. Avoiding the difficulty in estimating the numerical solutions in uniform norm, we prove that all the schemes are of the second‐order convergence in L2 norm by an induction argument. The unique solvability, stability, and an iterative algorithm are also discussed. A numerical example shows the correction of the theoretical analysis.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1340‐1363, 2011 |
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| Keywords: | convergence finite difference method 2D Ginzburg‐Landau equation solvability |
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