Optimal implicit exponentially-fitted Runge-Kutta methods

Implicit Runge-Kutta methods for first-order ODEs are considered and the pr oblem of how frequencies should be tuned in order to obtain the maximal ben efit from the exponential fitted versions of such algorithms is examined. T he key to the answer lies in the analysis of the behaviour of the error. A two-stage implicit Runge-Kutta method is particularly investigated. Formula e for optimal frequencies are produced; in that case the order of the metho d is increased by one unit. A numerical experiment illustrates the properti es of the developed algorithms. (C) 2001 Elsevier Science B.V. All rights r eserved.