  In this paper, we construct explicit nonstandard Runge-Kutta (ENRK) methods
which have higher accuracy order and preserve two important properties of
autonomous dynamical systems, namely, the positivity and linear stability.
These methods are based on the classical explicit Runge-Kutta methods, where
instead of the usual $h$ in the formulas there stands a function $\varphi (h)$.
It is proved that the constructed methods preserve the accuracy order of the
original Runge-Kutta methods. The numerical simulations confirm the validity of
the obtained theoretical results.
