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

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 \(\nu =\omega h\), where \(\omega \) is the frequency and h is the step size. Often, these coefficients exhibit a 0/0 indeterminate form when \(\nu \rightarrow 0\). 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.

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