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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2019, Volume 22, Number 3, Pages 243–259
DOI: https://doi.org/10.15372/SJNM20190301 (Mi sjvm713) 		 
This article is cited in 7 scientific papers (total in 7 papers)

A modification of numerical methods for stochastic differential equations with the first integral

T. A. Averinaab, K. A. Rybakovc

a Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia
c Moscow Aviation Institute (State Technical University), Volokolamskoye sh. 4, A-80, GSP-3, Moscow, 125993 Russia
Full-text PDF (4351 kB) Citations (7)
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DOI: https://doi.org/10.15372/SJNM20190301
Abstract: In this paper, stochastic differential equations (SDEs) with the first integral are considered. The exact solution of such SDEs belongs to a smooth manifold with probability 1. However, the numerical solution does not belong to the manifold, but it belongs to some of its neighborhood due to the numerical error. The main objective of the paper is to construct modified numerical methods for solving SDEs that preserve the first integral. In this study, exact solutions for three SDE systems with the first integral are obtained, and the proposed modification of numerical methods is tested on these systems.
Key words: numerical methods, statistical modeling, stochastic differential equations, manifold, first integral, projection.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0315-2016-0002
Russian Foundation for Basic Research 17-08-00530_a
This work was supported by Institute of Computational 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).
Received: 29.06.2018
Revised: 08.11.2018
Accepted: 07.09.2019
English version:
Numerical Analysis and Applications, 2019, Volume 12, Issue 3, Pages 203–218
DOI: https://doi.org/10.1134/S1995423919030017
Bibliographic databases:
Document Type: Article
UDC: 519.676
Language: Russian
Citation: T. A. Averina, K. A. Rybakov, “A modification of numerical methods for stochastic differential equations with the first integral”, Sib. Zh. Vychisl. Mat., 22:3 (2019), 243–259; Num. Anal. Appl., 12:3 (2019), 203–218
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    1. T. A. Averina, K. A. Rybakov, “Metody tipa Rozenbroka dlya resheniya stokhasticheskikh differentsialnykh uravnenii”, Sib. zhurn. vychisl. matem., 27:2 (2024), 123–145  mathnet  crossref
    2. T. A. Averina, K. A. Rybakov, “Rosenbrock-Type Methods for Solving Stochastic Differential Equations”, Numer. Analys. Appl., 17:2 (2024), 99  crossref
    3. Simon Schwarz, Michael Herrmann, Anja Sturm, Max Wardetzky, “Efficient Random Walks on Riemannian Manifolds”, Found Comput Math, 2023  crossref
    4. John Armstrong, Tim King, “Curved schemes for stochastic differential equations on, or near, manifolds”, Proc. R. Soc. A., 478:2262 (2022)  crossref
    5. Zh. Ma, Sh. Yu, Ya. Han, D. Guo, “Zeroing neural network for bound-constrained time-varying nonlinear equation solving and its application to mobile robot manipulators”, Neural Comput. Appl., 33:21 (2021), 14231–14245  crossref  mathscinet  isi  scopus
    6. Irina A. Kudryavtseva, Konstantin A. Rybakov, Smart Innovation, Systems and Technologies, 217, Applied Mathematics and Computational Mechanics for Smart Applications, 2021, 245  crossref
    7. T. A. Averina, K. A. Rybakov, “Using maximum cross section method for filtering jump-diffusion random processes”, Russ. J. Numer. Anal. Math. Model, 35:2 (2020), 55–67  crossref  mathscinet  zmath  isi  scopus
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