A variable-stepsize variable-order multistep method for the integration of perturbed linear problems Original Research Article

In 1971 Scheifele wrote the solution of a perturbed oscillator as an expansion in terms of a new set of functions, which extends the monomials in the Taylor series of the solution. Recently, Martı́n and Ferrándiz constructed a multistep code based on the Scheifele technique, and it was generalized by López and Martı́n for perturbed linear problems. However, the remarked codes are constant steplength methods, and efficient integrators must be able to change the steplength. In this paper we extend the ideas of Krogh from Adams methods to the algorithm proposed by López and Martı́n, and we show the advantages of the new code in perturbed problems.