Exponentially‐fitted algorithms: fixed or frequency dependent knot points?
- 15 March 2004
- journal article
- research article
- Published by Wiley in Applied Numerical Analysis & Computational Mathematics
- Vol. 1 (1) , 49-65
- https://doi.org/10.1002/anac.200310005
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.Keywords
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