Backward difference formulae: New multipliers and stability properties for parabolic equations

DOI10.1090/mcom3055zbMath1342.65179OpenAlexW2000486121MaRDI QIDQ2814437

Emmanuil Katsoprinakis, 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/mcom3055

zbMATH Keywords

stabilityBDF methodsnonlinear parabolic equationsmultipliersparabolic equationslinear parabolic equationsabstract Hilbert spaceimplicit-explicit BDF methodsenergy techniquebackward difference formulae methods

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Abstract parabolic equations (35K90) Initial-boundary value problems for second-order parabolic equations (35K20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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)

Related Items (12)

Energy stability of BDF methods up to fifth-order for the molecular beam epitaxial model without slope selection ⋮ Backward difference formulae for Kuramoto-Sivashinsky type equations ⋮ Stability and error estimates of local discontinuous Galerkin methods with implicit-explicit backward difference formulas up to fifth order for convection-diffusion equation ⋮ A new third-order energy stable technique and error estimate for the extended Fisher-Kolmogorov equation ⋮ Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations ⋮ On the uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for stiff hyperbolic relaxation systems and kinetic equations ⋮ The Energy Technique for the Six-Step BDF Method ⋮ Backward difference formulae: the energy technique for subdiffusion equation ⋮ Long-time Accurate Symmetrized Implicit-explicit BDF Methods for a Class of Parabolic Equations with Non-self-adjoint Operators ⋮ Stability properties of implicit–explicit multistep methods for a class of nonlinear parabolic equations ⋮ An analogue to the A$(\vartheta)$-stability concept for implicit-explicit BDF methods ⋮ Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation

Uses Software

• RODAS

Cites Work

• Fully implicit, linearly implicit and implicit-explicit backward difference formulae for quasi-linear parabolic equations
• On the equivalence of \(A\)-stability and \(G\)-stability
• Une méthode multipas implicite-explicite pour l'approximation des équations d'évolution paraboliques
• Implicit-explicit multistep methods for quasilinear parabolic equations
• Linearly implicit schemes for multi-dimensional Kuramoto–Sivashinsky type equations arising in falling film flows
• Backward difference time discretization of parabolic differential equations on evolving surfaces
• Computational Study of the Dispersively Modified Kuramoto–Sivashinsky Equation
• G-stability is equivalent toA-stability
• Linearly implicit methods for a semilinear parabolic system arising in two-phase flows
• Multiplier techniques for linear multistep methods
• Solving Ordinary Differential Equations II
• Stability of Implicit-Explicit Backward Difference Formulas For Nonlinear Parabolic Equations

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