A new approach to the construction of multirevolution methods and their implementation Original Research Article

A theoretical study of the multirevolution methods for numerical integration of oscillatory problems has been developed. A characterization of order of consistency via a generating function is given. The coefficients of the methods, formulated in a Lagrangian form, have been constructed for any order in a symbolic way making use of the generating function. The algorithm has been implemented together with a starting procedure, in order to optimize the number of function evaluations. Some numerical tests (a highly oscillatory problem and an artificial Earthʹs satellite) show the good behaviour (accuracy and saving in computing time) of such methods versus the classical variable-order and variable-step size multistep method.