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
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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