This talk is devoted to numerical methods for the nonlinear Dirac equation (NLDE) in the nonrelativistic limit regime with a small parameter which is inversely proportional to the speed of light. The solution to the NLDE is highly oscillatory in time in this regime, which causes severe burdens in numerical computation. We propose two kinds of uniformly accurate methods which can resolve the solution without any restriction to the time step. This is a joint work with Yongyong Cai.
