This article is cited in 8 papers

Numerical solution to stochastic differential equations on supercomputers

S. S. Artemiev^ab, V. D. Korneev<sup>ab

a</sup> Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University, Novosibirsk

Abstract: This paper deals with some issues of the dependence of the accuracy of algorithms for the numerical solutions of stochastic differential equations (SDEs) on the size of an ensemble of simulated trajectories. The problems of accuracy arise due to the necessity of estimating functionals of SDEs-solutions with an increasing dispersion, a strong asymmetry of solutions distributions, indeterminacy of the time of arrival of trajectories of solutions at the boundaries of given domains. The ways of parallelization of statistical algorithms on a multi-processor cluster are described. The results of numerical experiments obtained on the supercomputer of Siberian Supercomputer Center are presented.

Key words: stochastic differential equations, stochastic equations, parallelization, supercomputer, cluster.

UDC: 519.676

Received: 16.02.2010
Revised: 23.03.2010

 English version: Numerical Analysis and Applications, 2011, 4:1, 1–11

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