Analysis of simplifications of numerical schemes for Langevin equation, effect of variations in the correlation of augmentations

Turchenkov D.A., Turchenkov M.A.
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The possibility to simplify the integration of Langevin equation using the variation of correlation between augmentation was researched. The analytical expression for a set of numerical schemes is presented. It’s shown that asymptotic limits for squared velocity depend on step size. The region of convergence and the convergence orders were estimated. It turned out that the incorrect correlation between increments decrease the accuracy down to the level of first-order methods for schemes based on precise solution.

Keywords: diffusion, Langevin equation, stochastic differential equations, correlation, convergence order
Citation in English: Turchenkov D.A., Turchenkov M.A. Analysis of simplifications of numerical schemes for Langevin equation, effect of variations in the correlation of augmentations // Computer Research and Modeling, 2012, vol. 4, no. 2, pp. 325-338
Citation in English: Turchenkov D.A., Turchenkov M.A. Analysis of simplifications of numerical schemes for Langevin equation, effect of variations in the correlation of augmentations // Computer Research and Modeling, 2012, vol. 4, no. 2, pp. 325-338
DOI: 10.20537/2076-7633-2012-4-2-325-338
URL: http://crm-en.ics.org.ru/journal/article/1892/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
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