Difference methods for computing the Ginzburg‐Landau equation in two dimensions

In this article, three difference schemes of the Ginzburg‐Landau Equation in two dimensions are presented. In the three schemes, the nonlinear term is discretized such that nonlinear iteration is not needed in computation. The plane wave solution of the equation is studied and the truncation errors of the three schemes are obtained. The three schemes are unconditionally stable. The stability of the two difference schemes is proved by induction method and the time‐splitting method is analysized by linearized analysis. The algebraic multigrid method is used to solve the three large linear systems of the schemes. At last, we compute the plane wave solution and some dynamics of the equation. The numerical results demonstrate that our schemes are reliable and efficient. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 507–528, 2011py; 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 507–528, 2011