Ranjbar, HassanTorkzadeh, LeilaBaleanu, DumitruNouri, Kazem2024-01-242024-01-242023Ranjbar, Hassan;...et.al. (2023). "Simulating systems of Itô SDEs with split-step (α, β)-Milstein scheme", AIMS Mathematics, vol.8, No.2, pp.2576-2590.247369882473-6988https://hdl.handle.net/20.500.12416/6975In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (α, β)-Milstein scheme strongly convergence to the exact solution with order 1.0 in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters α, β. Finally, numerical examples illustrate the effectiveness of the theoretical results.eninfo:eu-repo/semantics/openAccessItô Stochastic Ordinary Differential EquationsMean-Square ConvergenceMean-Square StabilitySplit-Step Milstein SchemeArticle10.3934/math.2023133