Cooper, G. J. Stability of Runge-Kutta methods for trajectory problems. (English) Zbl 0624.65057 IMA J. Numer. Anal. 7, 1-13 (1987). 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 Cited in 85 Documents 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 Keywords:autonomous system; trajectories; Runge-Kutta methods; orbital stability; algebraic stability Citations:Zbl 0624.65056 PDFBibTeX XMLCite \textit{G. J. Cooper}, IMA J. Numer. Anal. 7, 1--13 (1987; Zbl 0624.65057) Full Text: DOI