Lattice Boltzmann model for the one-dimensional nonlinear Dirac equation.

In this paper, a lattice Boltzmann model for one-dimensional nonlinear Dirac equation is presented by using double complex-valued distribution functions and carefully selected equilibrium distribution functions. The effects of space and time resolutions and relaxation time on the accuracy and stability of the model are numerically investigated in detail. It is found that the model is of second-order accuracy in both space and time, and the order of accuracy is near 3.0 at lower grid resolution, which shows that the lattice Boltzmann method is an effective numerical scheme for the nonlinear Dirac equation.