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

Author

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

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.

Suggested Citation

  • Kong, Linghua & Luo, Yiyang & Wang, Lan & Chen, Meng & Zhao, Zhi, 2021. "HOC–ADI schemes for two-dimensional Ginzburg–Landau equation in superconductivity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 494-507.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:494-507
    DOI: 10.1016/j.matcom.2021.05.031
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