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A Modification of Numerical Methods for Stochastic Differential Equations with First Integrals

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Abstract

Stochastic differential equations (SDEs) with first integrals are considered. Exact solutions of such SDEs belong to smooth manifolds with probability 1. However, numerical solutions do not belong to the manifolds, but belong to their neighborhoods due to numerical errors. The main goal of this paper is to construct modified numerical methods for solving SDEs that have first integrals. In this study, exact solutions for three SDE systems with first integrals are obtained, and the modification of numerical methods is tested on these systems.

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Funding

This work was supported by Institute ofComputational Mathematics and Mathematical Geophysics, SB RAS (State target project no. 0315-2016-0002) and by the Russian Foundation for Basic Research (project no. 17-08-00530-a).

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia

    T. A. Averina

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    T. A. Averina

  3. Moscow Aviation Institute (State Technical University), Volokolamskoye sh. 4, A-80, GSP-3, Moscow, 125993, Russia

    K. A. Rybakov

Authors
  1. T. A. Averina
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  2. K. A. Rybakov
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Corresponding authors

Correspondence to T. A. Averina or K. A. Rybakov.

Additional information

Russian Text © The Author(s), 2019, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2019, Vol. 22, No. 3, pp. 243–258.

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Averina, T.A., Rybakov, K.A. A Modification of Numerical Methods for Stochastic Differential Equations with First Integrals. Numer. Analys. Appl. 12, 203–218 (2019). https://doi.org/10.1134/S1995423919030017

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  • DOI: https://doi.org/10.1134/S1995423919030017

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