A Transformed implicit Runge-Kutta Method

Abstract

Certain lmphclt Runge-Kutta methods are capable of being transformed into a form which makes the modified Newton iterates in their implementation capable of efficient computation. For the class of such methods considered, the transformations are given exphcltly, and it is shown how error estimates, as well as initial iterates for a succeeding step, can be expressed in terms of the transformed variables. © 1979, ACM. All rights reserved.