A quasi-randomized Runge-Kutta method
Authors:
Ibrahim Coulibaly and Christian Lécot
Journal:
Math. Comp. 68 (1999), 651-659
MSC (1991):
Primary 65L06; Secondary 65C05
DOI:
https://doi.org/10.1090/S0025-5718-99-01056-X
MathSciNet review:
1627781
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Abstract | References | Similar Articles | Additional Information
Abstract: We analyze a quasi-Monte Carlo method to solve the initial-value problem for a system of differential equations . The function
is smooth in
and we suppose that
and
are of bounded variation in
and that
is bounded in a neighborhood of the graph of the solution. The method is akin to the second order Heun method of the Runge-Kutta family. It uses a quasi-Monte Carlo estimate of integrals. The error bound involves the square of the step size as well as the discrepancy of the point set used for quasi-Monte Carlo approximation. Numerical experiments show that the quasi-randomized method outperforms a recently proposed randomized numerical method.
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Additional Information
Ibrahim Coulibaly
Affiliation:
Laboratoire de Mathématiques, Université de Savoie, Campus scientifique, 73376 Le Bourget-du-Lac cedex, France
Christian Lécot
Affiliation:
Laboratoire de Mathématiques, Université de Savoie, Campus scientifique, 73376 Le Bourget-du-Lac cedex, France
Email:
Christian.Lecot@univ-savoie.fr
DOI:
https://doi.org/10.1090/S0025-5718-99-01056-X
Keywords:
Runge-Kutta method,
quasi-Monte Carlo method,
discrepancy
Received by editor(s):
July 18, 1997
Article copyright:
© Copyright 1999
American Mathematical Society