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A new class of results for the algebraic equations of implicit Runge- Kutta processes. (English) Zbl 0738.65067
In the neighbourhood of an asymptotically stable equilibrium the discrete equations of a Runge-Kutta method have a unique solution for any step. In the neighbourhood of an attracting integral curve a unique solution exists for a sufficiently small step.

MSC:
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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