Accelerating numerical solution of stochastic differential equations with CUDA

M. Januszewski, M. Kostur
Institute of Physics, University of Silesia, 40-007 Katowice, Poland
Computer Physics Communications, Vol. 181, No. 1. (16 January 2010), pp. 183-188, arXiv:0903.3852 [physics.comp-ph] (23 Mar 2009)


   title={Accelerating numerical solution of stochastic differential equations with CUDA},

   author={Januszewski, M. and Kostur, M.},

   journal={Computer Physics Communications},








Numerical integration of stochastic differential equations is commonly used in many branches of science. In this paper we present how to accelerate this kind of numerical calculations with popular NVIDIA Graphics Processing Units using the CUDA programming environment. We address general aspects of numerical programming on stream processors and illustrate them by two examples: the noisy phase dynamics in a Josephson junction and the noisy Kuramoto model. In presented cases the measured speedup can be as high as 675x compared to a typical CPU, which corresponds to several billion integration steps per second. This means that calculations which took weeks can now be completed in less than one hour. This brings stochastic simulation to a completely new level, opening for research a whole new range of problems which can now be solved interactively.
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