  This paper focuses on the strong convergence rate of both Runge--Kutta
methods and simplified step-$N$ Euler schemes for stochastic differential
equations driven by multi-dimensional fractional Brownian motions with
$H\in(\frac12,1)$. Based on the continuous dependence of both stage values and
numerical schemes on driving noises, order conditions of Runge--Kutta methods
are proposed for the optimal strong convergence rate $2H-\frac12$. This
provides an alternative way to analyze the convergence rate of explicit schemes
by adding `stage values' such that the schemes are comparable with Runge--Kutta
methods. Taking advantage of this technique, the optimal strong convergence
rate of simplified step-N Euler scheme is obtained, which gives an answer to a
conjecture in $[3]$ when $H\in(\frac12,1)$. Numerical experiments verify the
theoretial convergence rate.
