Lattice Boltzmann model for the modified Burgers' equation

In this paper, a special lattice Boltzmann model is developed to solve the modified Burgers' equation. The maximum principle and the stability are proved. The model has been verified by several test examples. Excellent agreement is obtained between numerical predictions and the constructed asymptotic solutions or available numerical results. The careful numerical study indicates the computational efficiency and stability of the lattice Boltzmann method.