STABILITY REGIONS OF DISCRETE VARIABLE METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS,
TECHNISCHE HOCHSCHULE VIENNA (AUSTRIA) INSTITUT FUER NUMERISCHE MATHEMATIK
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The idea of strong stability is the following The effect of a perturbation in the finite-difference equation should not be worse than the effect of a corresponding perturbation in the differential equation to be solved numerically. For a given discretization scheme, a one-parameter family of regions in the complex domain is defined which permits to test for a given system of differential equations and a given stepsize whether strong stability prevails or not. Furthermore the shapes and sizes of the regions permit a comparison between the stability properties of various schemes. In the present report, a particular effort has been made to investigate the influences of the various alternatives in the algorithmic execution of a predictor-corrector method. The results are displayed in a large number of plots.
- Theoretical Mathematics