HOC–ADI schemes for two-dimensional Ginzburg–Landau equation in superconductivity

Linghua Kong, Yiyang Luo, Lan Wang, Meng Chen and Zhi Zhao

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 190, issue C, 494-507

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.

Keywords: Ginzburg–Landau equation; High-order compact scheme; Alternating direction implicit method; Extrapolation method (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:190:y:2021:i:c:p:494-507

DOI: 10.1016/j.matcom.2021.05.031

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