Stability of Variable-Step BDF2 and BDF3 Methods

DOI10.1137/21M1462398zbMath1501.65041arXiv2201.00527OpenAlexW4226324972MaRDI QIDQ5102238

Zhaoyi Li, Hong-lin Liao

Publication date: 6 September 2022

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.00527

zbMATH Keywords

stabilitydiscrete orthogonal convolution kernelsstep-ratio conditionvariable-step BDF formula

Mathematics Subject Classification ID

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)

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Cites Work

• Unnamed Item
• Unnamed Item
• Stability of multistep-methods on variable grids
• On the zero-stability of the 3-step BDF-formula on nonuniform grids
• Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection
• On the zero stability of the variable order variable stepsize BDF- formulas
• Mesh-robustness of an energy stable BDF2 scheme with variable steps for the Cahn-Hilliard model
• Solving Ordinary Differential Equations I
• The Convergence of Variable-Stepsize, Variable-Formula, Multistep Methods
• A Variable Stepsize, Variable Order Family of Low Complexity
• An adaptive BDF2 implicit time-stepping method for the phase field crystal model
• On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen--Cahn Equation
• Implicit-Explicit Multistep Methods for Hyperbolic Systems With Multiscale Relaxation
• Implicit-Explicit Linear Multistep Methods for Stiff Kinetic Equations
• Analysis of adaptive BDF2 scheme for diffusion equations
• On the zero-stability of variable stepsize multistep methods: The spectral radius approach