On the zero stability of the variable order variable stepsize BDF- formulas

DOI10.1007/BF01386395zbMath0696.65077OpenAlexW2073851030MaRDI QIDQ911237

Manuel Calvo, Rolf Dieter Grigorieff, T. Grande

Publication date: 1990

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133433

zbMATH Keywords

variable stepsizezero-stabilitystability boundsnonequidistant gridsvariable order backward differentiation formulas

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (10)

Discrete Energy Analysis of the Third-Order Variable-Step BDF Time-Stepping for Diffusion Equations ⋮ Linearly Implicit Multistep Methods for Time Integration ⋮ Convergence of the variable two-step BDF time discretisation of nonlinear evolution problems governed by a monotone potential operator ⋮ Fully-geometric mesh one-leg methods for the generalized pantograph equation: approximating Lyapunov functional and asymptotic contractivity ⋮ Efficient goal-oriented global error estimators for BDF methods using discrete adjoints ⋮ Stability of Variable-Step BDF2 and BDF3 Methods ⋮ Stability and convergence of the variable-step time filtered backward Euler scheme for parabolic equations ⋮ A\(_ 0\)-stability of variable stepsize BDF methods ⋮ Stability and error estimates for the variable step-size BDF2 method for linear and semilinear parabolic equations ⋮ A Variable Stepsize, Variable Order Family of Low Complexity

Uses Software

• DIFSUB

Cites Work

• Unnamed Item
• Stability of multistep-methods on variable grids
• On the zero-stability of the 3-step BDF-formula on nonuniform grids
• Zero-stability properties of the three-ordinate variable stepsize variable formula methods
• A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations

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