A Transformed implicit Runge-Kutta Method

  title={A Transformed implicit Runge-Kutta Method},
  author={John C. Butcher},
  journal={J. ACM},
Certain lmphclt Runge -Ku t t a methods are capable o f being t ransformed into a form which makes the modified Newton iterates in their implementa t ion capable o f efficient computa t ion . F o r the class o f such methods considered, the t ransformat ions are given exphcltly, and ~t is shown how error estimates, as well as initial iterates for a succeeding step, can be expressed in terms of the t ransformed variables 

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