A generalized Fourier–Hermite method for the Vlasov–Poisson system

generalized Fourier–Hermite semi-discretization for the Vlasov–Poisson equation is introduced. The formulation of the method includes as special cases the symmetrically-weighted and asymmetrically-weighted Fourier–Hermite methods from the literature. The numerical scheme is formulated as a weighted Galerkin method with two separate scaling parameters for the Hermite polynomial and the exponential part of the new basis functions. Exact formulas for the error in mass, momentum, and energy conservation of the method depending on the parameters are devised and L^2 stability is discussed. The numerical experiments show that an optimal choice of the additional parameter in the generalized method can yield improved accuracy compared to the existing methods, but also reveal the distinct stability properties of the symmetrically-weighted method.