A Splitting Spectral Method for the Nonlinear Dirac-Poisson Equations

A Splitting Spectral Method for the Nonlinear Dirac-Poisson Equations

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.

Author Details

Dandan Wang

Yong Zhang

Hanquan Wang