On the instability of methods for the integration of ordinary differential equations


In the numerical solution of a differential equation as a difference equation, the latter is usually of higher order and therefore has more solutions than the original differential equation. It may well be that some of these "extra" solutions grow faster than any solution of the given equation; in this case the computational solution has the tendency to follow one of these and has after a certain number of integration steps nothing to do with the original differential equation. The author gives some examples and a criterion for stability of integration methods. This criterion is then applied to some well-known integration formulas.

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