  In this paper a new concept, namely the critical predictable time $T_c$, is
introduced to give a more precise description of computed chaotic solutions of
nonlinear differential equations: it is suggested that computed chaotic
solutions are unreliable and doubtable when $ t > T_c$. This provides us a
strategy to detect reliable solution from a given computed result. In this way,
the computational phenomena, such as computational chaos (CC), computational
periodicity (CP) and computational prediction uncertainty, which are mainly
based on long-term properties of computed time series, can be completely
avoided. So, this concept also provides us a time-scale to determine whether or
not a particular time is long enough for a given nonlinear dynamic system.
Besides, the influence of data inaccuracy and various numerical schemes on the
critical predictable time is investigated in details by using symbolic
computation software as a tool. A reliable chaotic solution of Lorenz equation
in a rather large interval $0 \leq t < 1200$ non-dimensional Lorenz time units
is obtained for the first time. It is found that the precision of initial
condition and computed data at each time-step, which is mathematically
necessary to get such a reliable chaotic solution in such a long time, is so
high that it is physically impossible due to the Heisenberg uncertainty
principle in quantum physics. This however provides us a so-called "precision
paradox of chaos", which suggests that the prediction uncertainty of chaos is
physically unavoidable, and that even the macroscopical phenomena might be
essentially stochastic and thus could be described by probability more
economically.
