We present the results of fully 3-D hydrodynamic simulations of the gravitational collapse of isolated , turbulent molecular cloud cores .
Starting from initial states of hydrostatic equilibrium , we follow the collapse of both singular and nonsingular logatropic cores until the central protostar has accreted > 90 \% of the total available mass .
We find that , in the collapse of a singular core with access to a finite mass reservoir , the mass of the central protostar increases as M _ { acc } \propto t ^ { 4 } until it has accreted \sim 35 \% of the total available mass .
For nonsingular cores of fiducial masses 1 , 2.5 , and 5 M _ { \odot } , we find that protostellar accretion proceeds slowly prior to the formation of a singular density profile .
Immediately thereafter , the accretion rate in each case increases to \sim 10 ^ { -6 } M _ { \odot } yr ^ { -1 } , for cores with central temperature T _ { c } = 10 K and truncation pressure P _ { s } = 1.3 \times 10 ^ { 5 } k _ { B } cm ^ { -3 } K. It remains at that level until half the available mass has been accreted .
After this point , the accretion rate falls steadily as the remaining material is accreted onto the growing protostellar core .
We suggest that this general behaviour of the protostellar accretion rate may be indicative of evolution from the Class 0 to the Class I protostellar phase .