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Error analysis of Fourier–Legendre and Fourier–Hermite spectral-Galerkin methods for the Vlasov–Poisson system
We conduct a rigorous error analysis of the spectral-Galerkin methods for the 1D-1V Vlasov–Poisson system with the velocity variable in both finite and infinite domains. The estimates significantly improve the very limited existing results. We also provide numerical results to demonstrate the effectiveness of the analysed methods.