Stability properties of implicit–explicit multistep methods for a class of nonlinear parabolic equations

DOI10.1090/mcom/3070zbMath1342.65178OpenAlexW2063052319MaRDI QIDQ2814438

Georgios D. Akrivis

Publication date: 22 June 2016

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/mcom/3070

zbMATH Keywords

stabilitynonlinear parabolic equationsSwift-Hohenberg equationcomplex Ginzburg-Landau equationimplicit-explicit multistep methods

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Abstract parabolic equations (35K90) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Ginzburg-Landau equations (35Q56)

Related Items (3)

Numerical simulation of multidimensional nonlinear fractional Ginzburg-Landau equations ⋮ Stability and error estimates of local discontinuous Galerkin methods with implicit-explicit backward difference formulas up to fifth order for convection-diffusion equation ⋮ Long-time Accurate Symmetrized Implicit-explicit BDF Methods for a Class of Parabolic Equations with Non-self-adjoint Operators

Uses Software

• RODAS

Cites Work

• On the convergence of multistep methods for nonlinear stiff differential equations
• Vortices in the magnetic Ginzburg-Landau model
• Fully implicit, linearly implicit and implicit-explicit backward difference formulae for quasi-linear parabolic equations
• Une méthode multipas implicite-explicite pour l'approximation des équations d'évolution paraboliques
• \(A(\Theta)\)-stable approximation of abstract Cauchy problems
• Modified implicit--explicit BDF methods for nonlinear parabolic equations
• Implicit-explicit multistep methods for quasilinear parabolic equations
• Exact soliton solutions of the one-dimensional complex Swift-Hohenberg equation
• Backward difference formulae: New multipliers and stability properties for parabolic equations
• Backward difference time discretization of parabolic differential equations on evolving surfaces
• The world of the complex Ginzburg-Landau equation
• Asymptotic spatial patterns on the complex time-dependent Ginzburg-Landau equation
• Multiplier techniques for linear multistep methods
• Implicit-explicit multistep finite element methods for nonlinear parabolic problems
• Implicit–explicit multistep methods for nonlinear parabolic equations
• Solving Ordinary Differential Equations II
• Stability of Implicit-Explicit Backward Difference Formulas For Nonlinear Parabolic Equations
• Ginzburg-Landau vortices

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