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A PI stepsize control for the numerical solution of ordinary differential equations. (English) Zbl 0645.65039
Using ideas of control theory the authors derive a new step size control algorithm for the numerical integration of ordinary differential equations. The essential formula (Formula (11) on page 277) is astonishing simple and easy to implement. The proposed “proportional integral (PI)” algorithm is more robust than earlier ones and avoids oscillations of the step sizes when they are limited by numerical stability. It usually decreases the number of rejected steps. Several numerical experiments illustrate these properties.
Reviewer: E.Hairer

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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