On the numerical schemes for Langevin-type equations


Akat M., Kosker R. , Sirma A.

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, cilt.99, sa.3, ss.62-74, 2020 (ESCI İndekslerine Giren Dergi) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 99 Konu: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.31489/2020m3/62-74
  • Dergi Adı: BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS
  • Sayfa Sayıları: ss.62-74

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.