This paper is devoted to the construction and analysis of uniformly accurate nested Picard iterative integrators (NPI) for the Dirac equation in the nonrelativistic limit regime. In this regime, there is a dimensionless parameter ε ∈ (0, 1] inversely proportional to the speed of light and the equation admits propagating waves with O(1) wavelength in space and O(ε2) wavelength in time. To overcome the difficulty induced by the temporal ε dependent oscillation, we present the construction of several NPI methods which are uniformly first-, sec...
