On the numerical schemes for Langevin-type equations
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, vol.99, no.3, pp.62-74, 2020 (ESCI)
- Publication Type: Article / Article
- Volume: 99 Issue: 3
- Publication Date: 2020
- Doi Number: 10.31489/2020m3/62-74
- Journal Name: BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS
- Journal Indexes: Emerging Sources Citation Index (ESCI)
- Page Numbers: pp.62-74
- Open Archive Collection: AVESIS Open Access Collection
- Yıldız Technical University Affiliated: Yes
Abstract
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.