Abstract: It is already proved that the traditional fixed time step lattice Monte Carlo (LMC) algorithm can reproduce both the mean and the variance of the particle displacement exactly. However, there is always a non-zero skewness when there is a drift. To further improve the accuracy, a new LMC algorithm of biased diffusion model with five transition probabilities has been devised, which indeed reproduces the first three moments exactly. The valid scope of lattice step and time step can be determined numerically once the drift and the diffusivity are given. A new measurement is introduced to study the accuracy characteristics of the new algorithm. As a result, a particular lattice step can be discovered in which case the first step error is the maximum error in the simulation tests. Then, given the particular lattice step, the optimal time step can also be found to minimize the maximum error.

Key words: LMC algorithm, diffusion model, accuracy measurement, accuracy characteristic