  We study the convergence rates of the semi-discrete (SD) method originally
proposed in Halidias (2012), Semi-discrete approximations for stochastic
differential equations and applications, International Journal of Computer
Mathematics, 89(6). The SD numerical method was originally designed mainly to
reproduce qualitative properties of nonlinear stochastic differential equations
(SDEs). The strong convergence property of the SD method has been proved, but
except for certain classes of SDEs, the order of the method was not studied. We
study the order of L2-convergence and show that it can be arbitrarily close to
1/2. The theoretical findings are supported by numerical experiments.
