Generalized Laguerre Function-Generalized Hermite Function Mixed Approximation and Its Application

Abstract

The generalized Laguerre-generalized Hermite mixed spectral method is developed. Various orthogonal projections are investigated. Some mixed approximation results are established. As an example of their important applications, a mixed spectral scheme is proposed for two-dimensional non-isotropic heat conduction equation. Its convergence is proved. Numerical results demonstrate the high accuracy of this new spectral method.