In an effort to understand the anomalous behavior of the viscosity of liquid beryllium fluoride relative to other liquids in the strong/fragile classification we have carried out ion dynamics computer simulations of BeF2 over a temperature range which overlaps with the experimental viscosity data. Using the simple rigid ion potentials which seem to be suitable for the nonpolarizable ions of this substance, we obtain diffusivity data which are in good agreement with values obtained from the experimental viscosities when converted to diffusivities using the Eyring equation for jump transport processes. The diffusivity data show a highly anomalous fragile region of behavior at temperatures just above the limits of laboratory measurement, which reconciles the observed viscosity with that of other liquids. This strongly curved region is interpreted, using the Adams-Gibbs equation, in terms of a strongly negative liquid expansivity regime associated with a large heat capacity (hence strongly temperature-dependent entropy) regime. The negative expansivity regime ends in a,density maximum at 2000 K, beyond the reach of experiment, but a related density minimum expected at about 1250 K may be observable in sealed vessel experiments. In particular, a sudden similar to 30% rise in heat capacity, accessible to high temperature differential scanning calorimetry experiments, is predicted. The confirmation of this anomaly by laboratory experiments will bring much credibility to current speculations on the origin of the anomalous behavior of supercooled water. The reason for the displacement of the anomaly to high temperature relative to water is found in the parameters of the cooperative "bond lattice" model and is physically identified with contrasting changes in the low frequency density of vibrational states as temperature increases above the glass transition. Finally we show that the fragility of the BeF2, and also of the analogous SiO2, greatly exceed that of Lennard-Jones liquids in the computationally accessible regime, and then utilize this anomalous fragility to demonstrate the existence of nonlinear relaxation, behavior typical of fragile liquids, for BeF2. The fragile-liquid-to-strong-liquid crossover occurring at the limit of our computational range is a consequence of the thermodynamic anomaly in the liquid state. It is analogous to-but more pronounced than-that suggested earlier for liquid SiO2 in which it occurs in an experimentally quite inaccessible temperature range.