Pseudospectral method for non-isotropic heat transfer using mixed Hermite-Legendre interpolation

Abstract In this paper, we develop a new mixed pseudospectral method for heat transfer by using generalized Hermite functions and Legendre polynomials in unbounded domains. Fundamental to spectral methods for various unbounded-domain problems, we establish some basic results on the mixed generalized Hermite-Legendre interpolation. As an example, a new mixed generalized Hermite-Legendre pseudospectral scheme is provided for non-isotropic heat transfer. Its convergence is proved. Numerical results demonstrate the spectral accuracy of this approach.

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