Accuracy of New Lattice Monte Carlo Simulation Algorithm of Biased Diffusion Model

Authors

Zhengxiong Wu, College of Information System and Management, National University of Defense Technology, Changsha 410073, China;
Guo Gang, College of Information System and Management, National University of Defense Technology, Changsha 410073, China;
Duan Hong, College of Information System and Management, National University of Defense Technology, Changsha 410073, China;

Abstract

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.

Recommended Citation

Wu, Zhengxiong; Gang, Guo; and Hong, Duan (2020) "Accuracy of New Lattice Monte Carlo Simulation Algorithm of Biased Diffusion Model," Journal of System Simulation: Vol. 29: Iss. 10, Article 3.
DOI: 10.16182/j.issn1004731x.joss.201710003
Available at: https://dc-china-simulation.researchcommons.org/journal/vol29/iss10/3

First Page

2247

DOI Link

https://doi.org/10.16182/j.issn1004731x.joss.201710003

Last Page

2253

CLC

TP391.9

Recommended Citation

Wu Zhengxiong, Guo Gang, Duan Hong. Accuracy of New Lattice Monte Carlo Simulation Algorithm of Biased Diffusion Model[J]. Journal of System Simulation, 2017, 29(10): 2247-2253.

DOI

10.16182/j.issn1004731x.joss.201710003