Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/122339
Title: NUMERICAL METHODS AND COMPARISONS FOR THE DIRAC EQUATION IN THE NONRELATIVISTIC LIMIT REGIME
Authors: JIA XIAOWEI
Keywords: Dirac equation, nonlinear Dirac equation, FDTD methods, EWI-FP method, TSFP methods, uniformly accurate
Issue Date: 14-Aug-2015
Citation: JIA XIAOWEI (2015-08-14). NUMERICAL METHODS AND COMPARISONS FOR THE DIRAC EQUATION IN THE NONRELATIVISTIC LIMIT REGIME. ScholarBank@NUS Repository.
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.
URI: http://scholarbank.nus.edu.sg/handle/10635/122339
Appears in Collections:Ph.D Theses (Open)

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