A stability property of implicit Runge-Kutta methods

@article{Butcher1975ASP,
  title={A stability property of implicit Runge-Kutta methods},
  author={John C. Butcher},
  journal={BIT Numerical Mathematics},
  year={1975},
  volume={15},
  pages={358-361}
}
  • J. Butcher
  • Published 1 December 1975
  • Mathematics, Computer Science
  • BIT Numerical Mathematics
A class of implicit Runge-Kutta methods is shown to possess a stability property which is a natural extension of the notion ofA-stability for non-linear systems. 
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The concept of strongA-stability is defined. A class of stronglyA-stable Runge-Kutta processes is introduced. It is also noted that several classes of implicit Runge-Kutta processes defined by Ehle…
Implicit Runge-Kutta processes
Received November 1, 1962. Revised April 22, 1963. * If the function f(y) satisfies a Lipschitz condition and h is sufficiently small, then the equations defining g(1>, g(2), • • • , gw have a unique…
Error analysis for a class of methods for stiff non-linear initial value problems