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

T. A. Averina; K. A. Rybakov

doi:10.1134/S1995423919030017

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

T. A. Averina, K. A. Rybakov

Computational Mathematics Section

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

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	203-218
Number of pages	16
Journal	Numerical Analysis and Applications
Volume	12
Issue number	3
DOIs	https://doi.org/10.1134/S1995423919030017
Publication status	Published - 1 Jul 2019

Keywords

first integral
manifold
numerical methods
projection
statistical modeling
stochastic differential equations

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10.1134/S1995423919030017

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AU - Rybakov, K. A.

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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

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