2024/04/16 by Dongyang Liu, Liu, Dongyang, Minghui Song +3
Engineering · #FOS: Mathematics #Fluid Dynamics and Thin Films #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2404.10244
openalex publication_date 2024/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proposes an adaptive numerical method for stochastic delay differential equations (SDDEs) with a non-global Lipschitz drift term and a non-constant delay, building upon the work of Wei Fang and others. The method adapts the step size based on the growth of the drift term. Differing slightly from the conventional Euler-Maruyama format, this paper addresses the estimation of the delay term by substituting it with the numerically obtained solution closest to the left endpoint.This approach overcomes the challenge of numerical nodes not falling within the nodes after subtracting the delay. The paper proves the convergence of the numerical method for a class of non-global Lipschitz continuous SDDEs under the assumption that the step size function satisfies certain conditions.