Standard

A Modification of Numerical Methods for Stochastic Differential Equations with First Integrals. / Averina, T. A.; Rybakov, K. A.

In: Numerical Analysis and Applications, Vol. 12, No. 3, 01.07.2019, p. 203-218.

Research output: Contribution to journal › Article › peer-review

Harvard

Averina, TA & Rybakov, KA 2019, 'A Modification of Numerical Methods for Stochastic Differential Equations with First Integrals', Numerical Analysis and Applications, vol. 12, no. 3, pp. 203-218. https://doi.org/10.1134/S1995423919030017

APA

Averina, T. A., & Rybakov, K. A. (2019). A Modification of Numerical Methods for Stochastic Differential Equations with First Integrals. Numerical Analysis and Applications, 12(3), 203-218. https://doi.org/10.1134/S1995423919030017

Vancouver

Averina TA, Rybakov KA. A Modification of Numerical Methods for Stochastic Differential Equations with First Integrals. Numerical Analysis and Applications. 2019 Jul 1;12(3):203-218. doi: 10.1134/S1995423919030017

Author

Averina, T. A. ; Rybakov, K. A. / A Modification of Numerical Methods for Stochastic Differential Equations with First Integrals. In: Numerical Analysis and Applications. 2019 ; Vol. 12, No. 3. pp. 203-218.

BibTeX

@article{e94858236cb14c2f803d050899f4a6ad,
title = "A Modification of Numerical Methods for Stochastic Differential Equations with First Integrals",
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.",
keywords = "first integral, manifold, numerical methods, projection, statistical modeling, stochastic differential equations",
author = "Averina, {T. A.} and Rybakov, {K. A.}",
year = "2019",
month = jul,
day = "1",
doi = "10.1134/S1995423919030017",
language = "English",
volume = "12",
pages = "203--218",
journal = "Numerical Analysis and Applications",
issn = "1995-4239",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "3",

}

RIS

TY - JOUR

T1 - A Modification of Numerical Methods for Stochastic Differential Equations with First Integrals

AU - Averina, T. A.

AU - Rybakov, K. A.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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.

KW - first integral

KW - manifold

KW - numerical methods

KW - projection

KW - statistical modeling

KW - stochastic differential equations

UR - http://www.scopus.com/inward/record.url?scp=85071781454&partnerID=8YFLogxK

U2 - 10.1134/S1995423919030017

DO - 10.1134/S1995423919030017

M3 - Article

AN - SCOPUS:85071781454

VL - 12

SP - 203

EP - 218

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 3

ER -

ID: 21472812