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

T. A. Averina, K. A. Rybakov

Research output: Contribution to journalArticlepeer-review

3 Citations (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 languageEnglish
Pages (from-to)203-218
Number of pages16
JournalNumerical Analysis and Applications
Volume12
Issue number3
DOIs
Publication statusPublished - 1 Jul 2019

Keywords

  • first integral
  • manifold
  • numerical methods
  • projection
  • statistical modeling
  • stochastic differential equations

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