  We study a class of semi-implicit Taylor-type numerical methods that are easy
to implement and designed to solve multidimensional stochastic differential
equations driven by a general rough noise, e.g. a fractional Brownian motion.
In the multiplicative noise case, the equation is understood as a rough
differential equation in the sense of T.~Lyons. We focus on equations for which
the drift coefficient may be unbounded and satisfies a one-sided Lipschitz
condition only. We prove well-posedness of the methods, provide a full
analysis, and deduce their convergence rate. Numerical experiments show that
our schemes are particularly useful in the case of stiff rough stochastic
differential equations driven by a fractional Brownian motion.
