Computer simulation methods: in theoretical physics
Computer simulation methods: in theoretical physics
Orthogonal rational functions on a semi-infinite interval
Journal of Computational Physics
Polynomials for infinite-domain spectral elements
Journal of Computational Physics
Adaptive local overlapping grid methods for parabolic systems in two space dimensions
Journal of Computational Physics
The Hermite spectral method for Gaussian-type functions
SIAM Journal on Scientific Computing
The weighted Lp-norms of orthonormal polynomials for Freud weights
Journal of Approximation Theory
Vlasov simulations using velocity-scaled hermite representations
Journal of Computational Physics
Error estimation of Hermite spectral method for nonlinear partial differential equations
Mathematics of Computation
Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions
SIAM Journal on Numerical Analysis
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Applied Numerical Mathematics
Mixed legendre-hermite spectral method for heat transfer in an infinite plate
Computers & Mathematics with Applications
Generalized Hermite Spectral Method and its Applications to Problems in Unbounded Domains
SIAM Journal on Numerical Analysis
Generalized Hermite spectral method matching asymptotic behaviors
Journal of Computational and Applied Mathematics
A Hermite pseudospectral solver for two-dimensional incompressible flows on infinite domains
Journal of Computational Physics
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The convergence of a class of combined spectral-finite difference methods using Hermite basis, applied to the Fokker-Planck equation, is studied. It is shown that the Hermite based spectral methods are convergent with spectral accuracy in weighted Sobolev space. Numerical results indicating the spectral convergence rate are presented. A velocity scaling factor is used in the Hermite basis and is shown to improve the accuracy and effectiveness of the Hermite spectral approximation, with no increase in workload. Some basic analysis for the selection of the scaling factors is also presented.