scholarly journals Vortex collisions and energy-dissipation rates in the Ginzburg–Landau heat flow. Part I: Study of the perturbed Ginzburg–Landau equation

2007 ◽  
pp. 177-217 ◽  
Author(s):  
Sylvia Serfaty
Keyword(s):  
Energy Dissipation ◽  
Heat Flow ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Dissipation Rates ◽  
Flow Part

scholarly journals A Fourth Order Energy Dissipative Scheme for a Traffic Flow Model

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1238 ◽  
Author(s):  
Xiaowei Chen ◽  
Mingzhan Song ◽  
Songhe Song
Keyword(s):  
Energy Dissipation ◽  
Discrete System ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
New Energy ◽  
Long Time ◽  
Space Discretization ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral

We propose, analyze and numerically validate a new energy dissipative scheme for the Ginzburg–Landau equation by using the invariant energy quadratization approach. First, the Ginzburg–Landau equation is transformed into an equivalent formulation which possesses the quadratic energy dissipation law. After the space-discretization of the Fourier pseudo-spectral method, the semi-discrete system is proved to be energy dissipative. Using diagonally implicit Runge–Kutta scheme, the semi-discrete system is integrated in the time direction. Then the presented full-discrete scheme preserves the energy dissipation, which is beneficial to the numerical stability in long-time simulations. Several numerical experiments are provided to illustrate the effectiveness of the proposed scheme and verify the theoretical analysis.

Spiral Solutions of the Two-Dimensional Complex Ginzburg–Landau Equation

2001 ◽  
Vol 35 (2) ◽  
pp. 159-161
Author(s):  
Liu Shi-Da ◽  
Liu Shi-Kuo ◽  
Fu Zun-Tao ◽  
Zhao Qiang
Keyword(s):  
Landau Equation ◽  
Two Dimensional ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation
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