Year: 2023
Author: Dandan Wang, Yong Zhang, Hanquan Wang
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 4 : pp. 577–595
Abstract
We develop a splitting spectral method for the time-dependent nonlinear Dirac-Poisson (DP) equations. Through time splitting method, we split the time-dependent nonlinear DP equations into linear and nonlinear subproblems. To advance DP from time $t_n$ to $t_{n+1},$ the nonlinear subproblem can be integrated analytically, and linear Dirac and Poisson equation are well resolved by Fourier and Sine spectral method respectively. Compared with conventional numerical methods, our method achieves spectral accuracy in space, conserves total charge on the discrete level. Extensive numerical results confirm the spatial spectral accuracy, the second order temporal accuracy, and the $l^2$-stable property. Finally, an application from laser field is proposed to simulate the spin-flip phenomenon.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1025
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 4 : pp. 577–595
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Nonlinear Dirac-Poisson equations spectral method splitting method laser field spin-flip.