On the zero stability of the variable order variable stepsize BDF-Formulas
Copyright policy )On the zero stability of the variable order variable stepsize BDF-Formulas
The authors derive bounds for the mesh-size ratios \(h_{j+1}/h_ j\) of nonequidistant grids such that variable order backward differentiation formulas are zero-stable. In the case of 3-step formulas the results of the third author and \textit{P. J. Paes-Lemme} [BIT 24, 85-91 (1984; Zbl 0554.65052)] are substantially improved. Further results are presented for 4- and 5-step formulas. Finally, it is shown that introducing some additional assumptions on the stepsize variation, the stability bounds can be considerably improved.
- Technical University of Berlin Germany
- University of Zaragoza Spain
- DigiZeitschriften Germany
- Technical University of Berlin Germany
510.mathematics, variable stepsize, nonequidistant grids, zero-stability, variable order backward differentiation formulas, Nonlinear ordinary differential equations and systems, Stability and convergence of numerical methods for ordinary differential equations, Numerical methods for initial value problems involving ordinary differential equations, stability bounds, Article
510.mathematics, variable stepsize, nonequidistant grids, zero-stability, variable order backward differentiation formulas, Nonlinear ordinary differential equations and systems, Stability and convergence of numerical methods for ordinary differential equations, Numerical methods for initial value problems involving ordinary differential equations, stability bounds, Article
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