Ranjbar, HassanTorkzadeh, LeilaBaleanu, DumitruNouri, Kazem2024-10-242024-10-242022Ranjbar, Hassan...et al (2022). "Simulating systems of Ito? SDEs with split-step (?, ?)-Milstein scheme", AIMS MATHEMATICS, Vol. 8, No. 2, pp. 2576-2590.2473-6988http://hdl.handle.net/20.500.12416/8518In 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 (alpha, beta)-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 alpha, beta. Finally, numerical examples illustrate the effectiveness of the theoretical results.enginfo:eu-repo/semantics/openAccessItô Stochastic Ordinary Differential EquationsMean-Square ConvergenceMean-Square StabilitySplit-Step Milstein Schemearticle8225762590