NUMERICAL METHODS AND COMPARISONS FOR THE DIRAC EQUATION IN THE NONRELATIVISTIC LIMIT REGIME

JIA XIAOWEI

Publication

NUMERICAL METHODS AND COMPARISONS FOR THE DIRAC EQUATION IN THE NONRELATIVISTIC LIMIT REGIME

JIA XIAOWEI

Abstract

In my thesis first I compared the performances of several conventional numerical methods, like FDTD, EWI-FP and TSFP methods, in solving the Dirac and nonlinear Dirac equation in the nonrelativistic limit regime. Rigorous stability analysis and error estimates were established. Time step resolutions for different methods were also provided. Then I presented a uniformly accurate method based on multi-scale decomposition. A rigorous error estimate were presented with numerical results to show that the time step for this new method could be chosen independently in the nonrelativistic limit regime.