Mediterr. J. Math.
Springer International Publishing AG,
part of Springer Nature 2018
Improved Euler–Maruyama Method
for Numerical Solution of the Itˆo Stochastic
Diﬀerential Systems by Composite
Kazem Nouri, Hassan Ranjbar and Leila Torkzadeh
Abstract. In this paper, by composite previous-current-step idea, we
propose two numerical schemes for solving the Itˆo stochastic diﬀeren-
tial systems. Our approaches, which are based on the Euler–Maruyama
method, solve stochastic diﬀerential systems with strong sense. The
mean-square convergence theory of these methods are analyzed under
the Lipschitz and linear growth conditions. The accuracy and eﬃciency
of the proposed numerical methods are examined by linear and nonlinear
stochastic diﬀerential equations.
Mathematics Subject Classiﬁcation. Primary 60H10; Secondary 35D35,
Keywords. Stochastic diﬀerential systems, composite previous-current-
step idea, strong solution, Euler–Maruyama method, mean-square con-
In this paper, we consider two numerical methods for strong solution of the
Itˆo stochastic diﬀerential system,
dX(t)=f(t, X(t))dt +
This research was in part supported by a Grant from IPM (No. 94650074), and in part by
the Research Council of Semnan University.