  The development of Schramm--Loewner evolution (SLE) as the scaling limits of
discrete models from statistical physics makes direct simulation of SLE an
important task. The most common method, suggested by Marshall and Rohde
\cite{MR05}, is to sample Brownian motion at discrete times, interpolate
appropriately in between and solve explicitly the Loewner equation with this
approximation. This algorithm always produces piecewise smooth non
self-intersecting curves whereas SLE$_\kappa$ has been proven to be simple for
$\kappa\in[0,4]$, self-touching for $\kappa\in(4,8)$ and space-filling for
$\kappa\geq 8$. In this paper we show that this sequence of curves converges to
SLE$_\kappa$ for all $\kappa\neq 8$ by giving a condition on deterministic
driving functions to ensure the sup-norm convergence of simulated curves when
we use this algorithm.
