  Numerical algorithms are proposed for simulating the Brownian dynamics of
charged particles in an external magnetic field, taking into account the
Brownian motion of charged particles, damping effect and the effect of magnetic
field self-consistently. Performance of these algorithms is tested in terms of
their accuracy and long-time stability by using a three-dimensional Brownian
oscillator model with constant magnetic field. Step-by-step recipes for
implementing these algorithms are given in detail. It is expected that these
algorithms can be directly used to study particle dynamics in various dispersed
systems in the presence of a magnetic field, including polymer solutions,
colloidal suspensions and, particularly complex (dusty) plasmas. The proposed
algorithms can also be used as thermostat in the usual molecular dynamics
simulation in the presence of magnetic field.
