本文基于二阶傅里叶拟谱微分矩阵来近似二阶导数,得到一个泊松方程的全离散傅里叶拟谱格式. 运用FFT理论分析了该数值格式,推导了快速方法,最后进行了数值试验. 数值试验显示数值方法求解速度快、方便实施,且高精度,说明该数值方法为泊松方程的研究提供了一个有效的新工具.In this paper,based on second-order Fourier spectral differentiation matrix D2 to approximate the second derivative,we obtain a standard Fourier pseudospectral full-discretization for the Poisson equation. According to the relationship between the spectral differentiation matrix and discrete Fourier transform,we provide a fast algorithm for solving the discrete equations. Some numerical results are presented. By using the FFT algorithm,numerical experiments show that the new scheme is very effective for calculation speed and easy to practice,and it has the high accuracy,these imply that the Fourier pseudospectral method provides a new useful tool for the study of the Poisson equation
