This work mainly focuses on the numerical solution of the Poisson equation with the Dirichlet boundary conditions. Compared to the traditional 5-point finite difference method, the Chebyshev spectral method is applied. The numerical results show the Chebyshev spectral method has high accuracy and fast convergence;the more Chebyshev points are selected, the better the accuracy is. Finally, the error of two numerical results also verifies that the algorithm has high precision.
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