SUMMARYWe consider a class of multistage single-step methods introduced by Zienkicwicz ef al. ' and developed by Thomas and Gladwell.' From this class, we derive methods which are particularly suitable for the numerical solution of oscillatory problems. We propose a particular pair of methods which permit local error estimation while retaining a 'one-step' mode of operation. We discuss the implementation of this pair for both linear and nonlinear problems, and illustrate the discussion with numerical results.
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