  We are interested in the numerical approximation of non-linear stochastic
differential equations (SDEs) with solution in a certain domain. Our goal is to
construct explicit numerical schemes that preserve that structure. We
generalize the semi-discrete method \emph{Halidias N. and Stamatiou I.S.
(2016), On the numerical solution of some non-linear stochastic differential
equations using the Semi-Discrete method, Computational Methods in Applied
Mathematics,16(1)} and propose a numerical scheme, for which we prove a strong
convergence result, to a class of SDEs that appears in population dynamics and
ion channel dynamics within cardiac and neuronal cells. We furthermore extend
our scheme to a multidimensional case.
