Piffka..
Sorry, my account was incorrect about the discrepancy between the time of full moon and that of the maximum lunar eclipse. The discrepancy is caused by the difference between the antipodal point of the sun on the ecliptic (full moon) and that of the center of the shadow of the earth (maximum eclipse). And it is not related with the topocentric coordinates. Everything can be calculated with respect to the geocentric coordinates.
Lunar phases are calculated with reference to the ecliptic longitudes of the sun and the moon inside the hypothetical celestial sphere, and the ecliptic inside the sphere is looked upon as a circle. But the actual orbit of the earth around the sun and that of the moon is more close to ellipses than circles, and here arises the discrepancy between the results of calendrical calculation and those of eclipses.
This is somewhat similar to the difference between the well-tempered scales and the natural scales in the musical tone. Calendar is "well-tempered" while an eclipse is "natural."
To sum up, it will be more accurate to say that the maximum lunar eclipse occurs around the time of full moon but that the both do not necessarily coincide exactly.
A good software can be downloaded at the next link (free trial version). It can be used only on Windows box, which is not my default computer.
http://www.skymap.com/smp_eval.htm