On the numerical schemes for Langevin-type equations

Akat, M.; Kosker, Reşat; Sirma, A.

doi:10.31489/2020m3/62-74

On the numerical schemes for Langevin-type equations

Atıf İçin Kopyala

Akat M., Kosker R., Sirma A.

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
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.