Open AccessOn the numerical schemes for Langevin-type equations
Author(s) -
Muzaffer Akat,
Reşat Köşker,
Ali Sırma
Publication year - 2020
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2020m3/62-74
Subject(s) - discretization , mathematics , convergence (economics) , numerical analysis , numerical stability , type (biology) , stability (learning theory) , scheme (mathematics) , mathematical analysis , computer science , ecology , machine learning , economics , biology , economic growth
In this paper, a numerical approach is proposed based on the variation-of-constants formula for the numerical discretization Langevin-type equations. Linear and non-linear cases are treated separately. The proofs of convergence have been provided for the linear case, and the numerical implementation has been executed for the non-linear case. The order one convergence for the numerical scheme has been shown both theoretically and numerically. The stability of the numerical scheme has been shown numerically and depicted graphically.