User-Friendly Expressions of the Coefficients of Some Exponentially Fitted Methods

Abstract

The purpose of this work consists in reformulating the coefficients of some exponentially-fitted (EF) methods with the aim of avoiding numerical cancellations and loss of precision. Usually the coefficients of an EF method are expressed in terms of , where is the frequency and h is the step size. Often, these coefficients exhibit a 0/0 indeterminate form when . To avoid this feature we will use two sets of functions, called C and S , which have been introduced by Ixaru in [ 61 ]. We show that the reformulation of the coefficients in terms of these functions leads to a complete removal of the indeterminacy and thus the convergence of the corresponding EF method is restored. Numerical results will be shown to highlight these properties.