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QMC Methods for the solution of delay differential equations
Author(s) -
Kainhofer R.,
Tichy R.F.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310233
Subject(s) - mathematics , ordinary differential equation , interpolation (computer graphics) , hermite polynomials , argument (complex analysis) , runge–kutta methods , differential equation , mathematical analysis , computer science , animation , biochemistry , chemistry , computer graphics (images)
In this paper we will discuss the application of so‐called Runge Kutta Quasi‐Monte Carlo (RKQMC) methods (as proposed by Lécot, Koudiraty, Coulibaly, and Stengle) to heavily oscillating di.erential equations. The delayed argument is approximated by Hermite interpolation which transforms the equation into an ordinary differential equation so that the RKQMC methods can be applied. We will give a short discussion of this method and its advantages as well as its drawbacks, and give some more numerical results.