  The dissociative ionization of $H_2^+$ in a linearly polarized, 400 nm laser
pulse is simulated by solving a three-particle time-dependent Schr\"odinger
equation in full dimensionality without using any data from quantum chemistry
computation. The joint energy spectrum (JES) is computed using a time-dependent
surface flux (tSurff) method, the details of which are given. The calculated
ground energy is -0.597 atomic units and internuclear distance is 1.997 atomic
units if the kinetic energy term of protons is excluded, consistent with the
reported precise values from quantum chemistry computation. If the kinetic term
of the protons is included, the ground energy is -0.592 atomic units with an
internuclear distance 2.05 atomic units. Energy sharing is observed in JES and
we find peak of the JES with respect to nuclear kinetic energy release (KER) is
within $2\sim4$ eV, which is different from the previous two dimensional
computations (over 10 eV), but is close to the reported experimental values.
The projected energy distribution on azimuth angles shows that the electron and
the protons tend to dissociate in the direction of polarization of the laser
pulse.
