On the numerical schemes for Langevin-type equations


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Akat M., Kosker R. , Sirma A.

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, vol.99, no.3, pp.62-74, 2020 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 99 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.31489/2020m3/62-74
  • Title of Journal : BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS
  • Page Numbers: pp.62-74

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.