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

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 pape...

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Bibliographic Details
Published in:Numerical analysis and applications 2019-07, Vol.12 (3), p.203-218
Main Authors: Averina, T. A., Rybakov, K. A.
Format: Article
Language:English
Subjects:
Differential equations
Exact solutions
Integrals
Manifolds
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical methods
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Summary: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.
ISSN:1995-4239
1995-4247
DOI:10.1134/S1995423919030017