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Analysis of some finite difference schemes for two‐dimensional Ginzburg‐Landau equation
Author(s) -
Wang Tingchun,
Guo Boling
Publication year - 2011
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20588
Subject(s) - mathematics , norm (philosophy) , convergence (economics) , rate of convergence , partial differential equation , finite difference , finite difference method , stability (learning theory) , mathematical analysis , computer science , computer network , channel (broadcasting) , machine learning , political science , law , economics , economic growth
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 L 2 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