Split-step balanced θ-method for SDEs with non-globally Lipschitz continuous coefficients

Yufen Liu, Wanrong Cao and Yuelin Li

Applied Mathematics and Computation, 2022, vol. 413, issue C

Abstract: In this paper, a split-step balanced θ-method (SSBT) has been presented for solving stochastic differential equations (SDEs) under non-global Lipschitz conditions, where θ∈[0,1] is a parameter of the scheme. The moment boundedness and strong convergence of the numerical solution have been studied, and the convergence rate is 0.5. Moreover, under some conditions it is proved that the SSBT scheme can preserve the exponential mean-square stability of the exact solution when θ∈(1/2,1] for every step size h>0. Numerical examples verify the theoretical findings.

Keywords: Nonlinear problems; The balanced method; Strong convergence; Exponential stability; Mean-square contraction (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:413:y:2022:i:c:s0096300321005269

DOI: 10.1016/j.amc.2021.126437

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