Geodesic
A modification of numerical methods for stochastic differential equations with the first integral
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 3, pp. 243-259

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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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     author = {T. A. Averina and K. A. Rybakov},
     title = {A modification of numerical methods for stochastic differential equations with the first integral},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {243--259},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2019_22_3_a0/}
}
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T. A. Averina; K. A. Rybakov. A modification of numerical methods for stochastic differential equations with the first integral. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 3, pp. 243-259. http://geodesic.mathdoc.fr/item/SJVM_2019_22_3_a0/