On the Stability of Interpolatory Variable-Stepsize Adams Methods in Nordsieck Form
Copyright policy )On the Stability of Interpolatory Variable-Stepsize Adams Methods in Nordsieck Form
In the existing ODE codes stepsize controls are incorporated. In order to ensure the stability of the integration process restrictions on the stepsize variation must be imposed. The authors consider various strategies for the stepsize selection and corresponding conditions for the allowable ratio \(h_{j+1}/h_ j\) of consecutive stepsize for the Adams methods in Nordsieck form. It is shown that for predictor-corrector methods the same bounds apply. The results extend and partly correct corresponding ones obtained by \textit{L. W. Jackson} and \textit{R. D. Skeel} [ibid. 20, 840-853 (1983; Zbl 0514.65058)]. Recently, the authors also studied the corresponding questions for the Nordsieck BDF methods [ibid. 24, 844-854 (1987; Zbl 0644.65042)].
- University of Zaragoza Spain
Adams methods in Nordsieck form, stepsize controls, stepsize selection, predictor-corrector methods, Nonlinear ordinary differential equations and systems, stability, stepsize variation, Stability and convergence of numerical methods for ordinary differential equations, Numerical methods for initial value problems involving ordinary differential equations
Adams methods in Nordsieck form, stepsize controls, stepsize selection, predictor-corrector methods, Nonlinear ordinary differential equations and systems, stability, stepsize variation, Stability and convergence of numerical methods for ordinary differential equations, Numerical methods for initial value problems involving ordinary differential equations
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