On the numerical schemes for Langevin-type equations - Akat, M.; Kosker, R.; Sirma, A. (KARAGANDA STATE UNIV, 2020)
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.
Keywords: difference schemes; stochastic oscillators; Langevin equation; variation of constants; Mathematics