T. A. Averina, K. A. Rybakov, “A modification of numerical methods for stochastic differential equations with the first integral”, Sib. Zh. Vychisl. Mat., 2019, Volume 22, Number 3,Pages <nobr>243

This article is cited in 7 papers

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

T. A. Averina^ab, K. A. Rybakov^c

^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

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.

UDC: 519.676

Received: 29.06.2018
Revised: 08.11.2018
Accepted: 07.09.2019

DOI: 10.15372/SJNM20190301