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Volume 20, Issue 4
A Splitting Spectral Method for the Nonlinear Dirac-Poisson Equations

Dandan Wang, Yong Zhang & Hanquan Wang

DOI: 10.4208/ijnam2023-1025

Int. J. Numer. Anal. Mod., 20 (2023), pp. 577-595.

Published online: 2023-05

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  • 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.

  • Keywords

Nonlinear Dirac-Poisson equations, spectral method, splitting method, laser field, spin-flip.

  • AMS Subject Headings

65M70, 65M12, 81-08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-20-577, author = {Wang , DandanZhang , Yong and Wang , Hanquan}, title = {A Splitting Spectral Method for the Nonlinear Dirac-Poisson Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2023}, volume = {20}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2023-1025}, url = {http://global-sci.org/intro/article_detail/ijnam/21717.html} }
TY - JOUR T1 - A Splitting Spectral Method for the Nonlinear Dirac-Poisson Equations AU - Wang , Dandan AU - Zhang , Yong AU - Wang , Hanquan JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 577 EP - 595 PY - 2023 DA - 2023/05 SN - 20 DO - http://doi.org/10.4208/ijnam2023-1025 UR - https://global-sci.org/intro/article_detail/ijnam/21717.html KW - Nonlinear Dirac-Poisson equations, spectral method, splitting method, laser field, spin-flip. AB -

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.

Dandan Wang, Yong Zhang & Hanquan Wang. (2023). A Splitting Spectral Method for the Nonlinear Dirac-Poisson Equations. International Journal of Numerical Analysis and Modeling. 20 (4). 577-595. doi:10.4208/ijnam2023-1025
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