The Hermite spectral method for Gaussian-type functions
SIAM Journal on Scientific Computing
SIAM Journal on Computing
Inviscid axisymmetrization of an elliptical vortex
Journal of Computational Physics
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
Numerical Recipes in C++: the art of scientific computing
Numerical Recipes in C++: the art of scientific computing
Combined Hermite spectral-finite difference method for the Fokker-Planck equation
Mathematics of Computation
Theoretical Computer Science
SIAM Journal on Scientific Computing
Journal of Scientific Computing
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The Hermite pseudospectral method is applied to solve the Navier-Stokes equations on a two-dimensional infinite domain. The feature of Hermite function allows us to adopt larger time steps than other spectral methods, but also leads to some extra computation when the stream function is calculated from the vorticity field. The scaling factor is employed to increase the resolution within the region of our main interest, and the aliasing error is fully removed by the 2/3-rule. Several traditional numerical experiments are performed with high accuracy, and some related future work on physical applications of this program is also discussed.