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 |
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Pages (from-to) | 203-218 |
Number of pages | 16 |
Journal | Numerical Analysis and Applications |
Volume | 12 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Jul 2019 |
Keywords
- first integral
- manifold
- numerical methods
- projection
- statistical modeling
- stochastic differential equations