  We consider a dynamical system, defined by a system of autonomous
differential equations, on $\Omega\subset\mathbb{R}^n$. By using Mickens' rule
on the nonlocal approximation of nonlinear terms, we construct an implicit
Nonstandard Finite Difference (NSFD) scheme that, under an existence and
uniqueness condition, is an explicit time reversible scheme. Apart from being
elementary stable, we show that the NSFD scheme is of second-order and
domain-preserving, thereby solving a pending problem on the construction of
higher-order nonstandard schemes without spurious solutions, and extending the
tangent condition to discrete dynamical systems. It is shown that the new
scheme applies directly for mass action-based models of biological and chemical
processes.
