Laguerre spectral approximation of elliptic problems in exterior domains
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
The Hermite spectral method for Gaussian-type functions
SIAM Journal on Scientific Computing
Error estimation of Hermite spectral method for nonlinear partial differential equations
Mathematics of Computation
Combined Hermite spectral-finite difference method for the Fokker-Planck equation
Mathematics of Computation
Hermite Spectral Methods with a Time-Dependent Scaling for Parabolic Equations in Unbounded Domains
SIAM Journal on Numerical Analysis
Generalized Laguerre Interpolation and Pseudospectral Method for Unbounded Domains
SIAM Journal on Numerical Analysis
A Spectral Viscosity Method Based on Hermite Functions for Nonlinear Conservation Laws
SIAM Journal on Numerical Analysis
Mixed legendre-hermite spectral method for heat transfer in an infinite plate
Computers & Mathematics with Applications
Generalized Hermite spectral method matching asymptotic behaviors
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
| Hi-index | 0.00 |
In this paper, we develop a spectral method based on generalized Hermite functions with weight $\chi(x)\equiv1$. We also establish some basic results on generalized Hermite orthogonal approximations, which play an important role in spectral methods. As examples, the generalized Ginzburg-Landau equation in a population problem and an elliptic equation with a harmonic potential are considered. Related spectral schemes are proposed, and their convergence is proved. Numerical results demonstrate the spectral accuracy of this approach.