Exponentially-fitted algorithms: fixed or frequency dependent knot points?

Abstract

Exponentially-fitted algorithms are constructed for the derivation of Gauss formulae and implicit Runge-Kutta methods of collocation type making them tuned for oscillatory (or exponential) functions. The weights and the abscissas of these formulae can depend naturally on the frequency ω by the very construction. For twopoints Gauss formulae and two-step Runge-Kutta methods a detailed study of the obtained results is made. In particular the difference in the numerical application of these algorithms with fixed points and/or frequency dependent nodes is analysed. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)