University of Tabriz Computational Methods for Differential Equations 2345-3982 11 4 2023 07 01 An explicit split-step truncated Milstein method for stochastic differential equations 676 695 15639 10.22034/cmde.2022.51249.2132 EN Amir Haghighi Department of Mathematics, Faculty of Science, Razi University, Kermanshah 67149, Iran. Journal Article 2022 04 22 In this paper, we propose an explicit split-step truncated Milstein method for stochastic differential equations (SDEs) with commutative noise. We discuss the mean-square convergence properties of the new method for numerical solutions of a class of highly nonlinear SDEs in a finite time interval. As a result, we show that the strong convergence rate of the new method can be arbitrarily close to one under some additional conditions. Finally, we use an illustrative example to highlight the advantages of our new findings in terms of both stability and accuracy compared to the results in Guo et al. (2018). https://cmde.tabrizu.ac.ir/article_15639_0374edec83e9f9ace24d55d461e071b5.pdf