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 - <p style="text-align: justify;">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.</p>