Abstract
In this paper, we apply the high-order compact scheme coupled with alternating direction implicit (HOC–ADI) method to solve the two-dimensional Ginzburg–Landau (2D GL) equation. Five HOC–ADI schemes with second order accuracy in time and fourth order in space are proposed for 2D GL equation. Scheme I and Scheme II are both nonlinear, which need nonlinear iteration.To overcome this shortcoming, Scheme III and Scheme IV are proposed in order to avoid nonlinear iteration. With the three-level ADI scheme and the method of extrapolation, we obtain a linearized scheme V. Some numerical experiments are shown to testify and compare the superiority of the new numerical schemes.
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