High-order compact ADI method using predictor–corrector scheme for 2D complex Ginzburg–Landau equation

Shokri, Ali; Afshari, Fatemeh S.

doi:10.1016/j.cpc.2015.08.005

Cited by 13 publications

(3 citation statements)

References 45 publications

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“…Li considered decoupled mixed finite element method in a nonsmooth domain [21,22]. Shoki et al developed a kind of meshless methods by using radial basis functions [27]. Wang reported an efficient Chebyshev-Tau spectral method [29].…”

mentioning

confidence: 99%

Efficient numerical schemes for two-dimensional Ginzburg-Landau equation in superconductivity

Kong¹,

Kuang²,

Wang³

2019

Discrete &Amp; Continuous Dynamical Systems - B

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The objective of this paper is to propose some high-order compact schemes for two-dimensional Ginzburg-Landau equation. The space is approximated by high-order compact methods to improve the computational efficiency. Based on Crank-Nicolson method in time, several temporal approximations are used starting from different viewpoints. The numerical characters of the new schemes, such as the existence and uniqueness, stability, convergence are investigated. Some numerical illustrations are reported to confirm the advantages of the new schemes by comparing with other existing works. In the numerical experiments, the role of some parameters in the model is considered and tested.

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mentioning

confidence: 99%

Efficient numerical schemes for two-dimensional Ginzburg-Landau equation in superconductivity

Kong¹,

Kuang²,

Wang³

2019

Discrete &Amp; Continuous Dynamical Systems - B

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“…Applying integration by parts to (11), and replacing the fluxes at the interfaces by the corresponding numerical fluxes, we obtain…”

Section: Ldg Scheme For Ginzburg-landau Equationmentioning

confidence: 99%

“…The various kinds of numerical methods can be found for simulating solutions of the nonlinear Ginzburg-Landau problems [3][4][5][6][7][8][9][10][11]. The local discontinuous Galerkin (LDG) method is famous for high accuracy properties and extreme flexibility [12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Local Discontinuous Galerkin Method for Nonlinear Ginzburg- Landau Equation

Aboelenen¹

2018

Differential Equations - Theory and Current Research

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The Ginzburg-Landau equation has been applied widely in many fields. It describes the amplitude evolution of instability waves in a large variety of dissipative systems in fluid mechanics, which are close to criticality. In this chapter, we develop a local discontinuous Galerkin method to solve the nonlinear Ginzburg-Landau equation. The nonlinear Ginzburg-Landau problem has been expressed as a system of low-order differential equations. Moreover, we prove stability and optimal order of convergence Oh Nþ1 ÀÁ for Ginzburg-Landau equation where h and N are the space step size and polynomial degree, respectively. The numerical experiments confirm the theoretical results of the method.

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A meshless method for solving nonlinear variable-order fractional Ginzburg–Landau equations on arbitrary domains

Li,

Chen

2022

J. Appl. Math. Comput.

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High-order compact ADI method using predictor–corrector scheme for 2D complex Ginzburg–Landau equation

Cited by 13 publications

References 45 publications

Efficient numerical schemes for two-dimensional Ginzburg-Landau equation in superconductivity

Efficient numerical schemes for two-dimensional Ginzburg-Landau equation in superconductivity

Local Discontinuous Galerkin Method for Nonlinear Ginzburg- Landau Equation

A meshless method for solving nonlinear variable-order fractional Ginzburg–Landau equations on arbitrary domains

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