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Stability of Runge-Kutta methods for trajectory problems. (English) Zbl 0624.65057

The trajectories to which the title of the paper refers are those defined in m-dimensional space by a solution of m autonomous differential equations. The author first introduces a particular nonlinear model problem which gives typical trajectories. He then shows that some Runge- Kutta methods possess a property which ensures that the solution for this model problem lies on the same surface as the trajectory. This property, referred to as orbital stability, is related to algebraic stability, a topic to which the author has contributed elsewhere [ibid. 6, 325-330 (1986; reviewed above)].
Reviewer: J.Oliver

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems

Citations:

Zbl 0624.65056
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