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 ν= ωh, where ω is the frequency and h is the step size. Often, these coefficients exhibit a 0/0 indeterminate form when ν→ 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.
User-Friendly Expressions of the Coefficients of Some Exponentially Fitted Methods
D'Ambrosio R.;
2020
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 ν= ωh, where ω is the frequency and h is the step size. Often, these coefficients exhibit a 0/0 indeterminate form when ν→ 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
