Numerical methods for nonlinear Dirac equation
TL;DR: Comparisons show that the high-order accurate OS schemes may compete well with other numerical schemes discussed here in terms of the accuracy and the efficiency, and the interaction dynamics of two NLD solitary waves depend on the exponent power of the self-interaction in the NLD equation.
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About: This article is published in Journal of Computational Physics. The article was published on 15 Jul 2013. and is currently open access. The article focuses on the topics: Conservation law & Nonlinear Dirac equation.
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Citations
Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime
TL;DR: In this article, the authors present several numerical methods and establish their error estimates for the discretization of the nonlinear Dirac equation (NLDE) in the nonrelativistic limit regime, involving a small dimensionless parameter 0 < e ≤ 1 which is inversely proportional to the speed of light.
Numerical Methods and Comparison for the Dirac Equation in the Nonrelativistic Limit Regime
TL;DR: In this article, the authors analyzed rigorously error estimates and compare numerically spatial/temporal resolution of various numerical methods for the discretization of the Dirac equation in the nonrelativistic limit regime, involving a small dimensionless parameter.
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A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in ( 1+1)D
TL;DR: Simulations of Gaussian wave packets, leaving the computational domain without reflection, demonstrate the quality of the DTBCs numerically, as well as the importance of a faithful representation of the energy-momentum dispersion relation on a grid.
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A uniformly accurate multiscale time integrator pseudospectral method for the Klein-Gordon equation in the nonrelativistic limit regime
TL;DR: A multiscale time integrator Fourier pseudospectral method for the Dirac equation with a dimensionless parameter $\varepsilon\in(0,1]$ which is inversely proportional to the speed of light is proposed and rigourously analyzed.
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A split-step numerical method for the time-dependent Dirac equation in 3-D axisymmetric geometry
TL;DR: The time evolution of Gaussian wave packets is studied, and the eigenstates of hydrogen-like systems are evaluated by using a spectral method, and three-dimensional simulations of relativistic laser–matter interactions are presented, using the Dirac equation.
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