  Electron collisions, described by stochastic differential equations (SDEs),
were simulated using a second-order weak convergence algorithm. Using
stochastic analysis, we constructed an SDE for energetic electrons in Lorentz
plasma to incorporate the collisions with heavy static ions as well as
background thermal electrons. Instead of focusing on the errors of each
trajectory, we initiated from the weak convergence condition to directly
improve the numerical accuracy of the distribution and its moments. A
second-order weak convergence algorithm was developed, estimated the order of
the algorithm in a collision simulation case, and compared it with the results
obtained using the Euler-Maruyama method and the Cadjan-Ivanov method. For a
fixed error level, the second order method largely reduce the computation time
compared to the Euler-Maruyama method and the Cadjan-Ivnaov method. Finally,
the backward runaway phenomenon was numerically studied and the probability of
this runaway was calculated using the new method.
