Abstract
AbstractExponentially‐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)
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