A modification of numerical methods for stochastic differential equations with the first integral
T.A. Averina1,2, K.A. Rybakov3
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russia
2Novosibirsk State University, Novosibirsk, Russia
3Moscow Aviation Institute, Moscow, Russia
Keywords: численные методы, статистическое моделирование, стохастические дифференциальные уравнения, многообразие, первый интеграл, проекция, numerical methods, statistical modeling, stochastic differential equations, manifold, first integral, projection
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.
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