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

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Author(s) : Etienne Emmrich

The paper is published : J. Appl. Math. & Computing

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 the two-step backward differentiation formula with variable step sizes is analysed. Stability as well as optimal smooth data error estimates are derived if the ratios of adjacent step sizes are bounded from above by 1.91.

Keywords : semilinear parabolic problem; time discretization; backward differentiation formula; non-uniform grid; stability; error estimate