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Preprint 703-2000

Stability and error of the variable two-step BDF for parabolic problems

Source file is available as :   Postscript Document

Author(s) : Etienne Emmrich

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 703-2000

MSC 2000

65M12 Stability and convergence of numerical methods
65J15 Equations with nonlinear operators
35K90 Abstract parabolic evolution equations
47J35 Nonlinear evolution equations

Abstract :
The temporal discretisation of a moderate semilinear parabolic problem in an abstract setting by means of the two-step backward differentiation formula with variable step sizes is analysed. Stability as well as optimal error estimates are derived for step size ratios bounded by 1.91.

Keywords : Semilinear parabolic problem, time discretisation, backward differentiation formula, non-uniform grid, stability, error estimate

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