Long Time Behavior of Difference Approximations for the Two-Dimensional Complex Ginzburg–Landau Equation

DOI10.1080/01630563.2010.510974zbMath1410.65335OpenAlexW1963818985WikidataQ57664955 ScholiaQ57664955MaRDI QIDQ3068653

Lei Zhang

Publication date: 17 January 2011

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2010.510974

zbMATH Keywords

Ginzburg-Landau equationglobal attractorsstability and convergencesemi-explicit difference approximation

Mathematics Subject Classification ID

Attractors (35B41) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical problems in dynamical systems (65P99) Ginzburg-Landau equations (35Q56)

Related Items (6)

The construction of higher-order numerical approximation formula for Riesz derivative and its application to nonlinear fractional differential equations (I) ⋮ A new compact finite difference scheme for solving the complex Ginzburg-Landau equation ⋮ A linearized high-order difference scheme for the fractional Ginzburg-Landau equation ⋮ The Numerical Analysis of the Long Time Asymptotic Behavior for Lotka-Volterra Competition Model with Diffusion ⋮ An unconditionally stable linearized difference scheme for the fractional Ginzburg-Landau equation ⋮ An implicit midpoint difference scheme for the fractional Ginzburg-Landau equation

Cites Work

• Dimension of the attractors associated to the Ginzburg-Landau partial differential equation
• Localization and approximation of attractors for the Ginzburg-Landau equation
• Infinite-dimensional dynamical systems in mechanics and physics.
• On the initial-value problem for the generalized two-dimensional Ginzburg-Landau equation
• Low-dimensional behaviour in the complex Ginzburg-Landau equation
• Finite-dimensional models of the Ginsburg-Landau equation
• Attractors and dimensions for discretizations of a weakly damped Schrödinger equation and a Sine-Gorden equation
• The Global Dynamics of Discrete Semilinear Parabolic Equations
• Regularity of solutions and the convergence of the galerkin method in the ginzburg-landau equation
• Attractors and Inertial Manifolds for Finite-Difference Approximations of the Complex Ginzburg--Landau Equation
• A Nonstiff Euler Discretization of the Complex Ginzburg--Landau Equation in One Space Dimension
• Long time stability and convergence for fully discrete nonlinear galerkin methods
• Discrete gevrey regularity attractors and uppers–semicontinuity for a finite difference approximation to the ginzburg–landau equation
• A non-linear instability theory for a wave system in plane Poiseuille flow

This page was built for publication: Long Time Behavior of Difference Approximations for the Two-Dimensional Complex Ginzburg–Landau Equation