Implicit Runge-Kutta processes

  title={Implicit Runge-Kutta processes},
  author={John C. Butcher},
  journal={Mathematics of Computation},
  • J. Butcher
  • Published 1964
  • Mathematics
  • Mathematics of Computation
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 solution which may be found by iteration (see Appendix). t It will be assumed throughout that f (y) and all its derivatives exist and are continuous so that the Taylor expansions for y and y may be terminated at any term with an error of the same order as the first term omitted. 50 

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