On the numerical schemes for Langevin-type equations
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, cilt.99, sa.3, ss.62-74, 2020 (ESCI)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 99 Sayı: 3
- Basım Tarihi: 2020
- Doi Numarası: 10.31489/2020m3/62-74
- Dergi Adı: BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
- Sayfa Sayıları: ss.62-74
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
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.