Exponentially fitted fifth-order two-step peer explicit methods

The so called peer methods for the numerical solution of Initial Value Problems (IVP) in ordinary differential systems were introduced by R. Weiner et al [6, 7, 11, 12, 13] for solving different types of problems either in sequential or parallel computers. In this work, we study exponentially fitted three-stage peer schemes that are able to fit functional spaces with dimension six. Finally, some numerical experiments are presented to show the behaviour of the new peer schemes for some periodic problems

Exponential fitting techniques for the solution of stiff problems with explicit methods

In this talk the use of exponentially fitting techniques to solve, by means of explicit RK methods, stiff problems is analyzed. The construction of explicit methods with a stability region adequate for problems in which the spectrum has a gap is studied. The order stiff of the proposed methods is also considered, obtaining conditions that guarantee a prefixed stiff order. Numerical experiments showing the performance of the methods are presented

Functionally fitted explicit two step peer methods

In this paper we study functionally fitted methods based on explicit two step peer formulas. We show that with s stages it is possible to get explicit fitted methods for fitting spaces of high dimension 2s, by proving the existence and uniqueness of such formulas. Then, weobtain particular methods with 2 and 3 stages fitted to trigonometric and exponential spaces of dimension 4 and 6 respectively. By means of several numerical examples we show the performance of the obtained methods, comparing them to fitted Adams-Bashforth-Moulton methods with the same order

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 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. 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