TY - JOUR T1 - Mixed Spectral Method for Heat Transfer Using Generalised Hermite Functions and Legendre Polynomials JO - East Asian Journal on Applied Mathematics VL - 4 SP - 448 EP - 465 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.231015.240816a UR - https://global-sci.org/intro/article_detail/eajam/10812.html KW - The scaled generalised Hermite functions, mixed spectral method, anisotropic heat transfer, unbounded domains. AB -

We propose a mixed spectral method for heat transfer in unbounded domains, using generalised Hermite functions and Legendre polynomials. Some basic results on the mixed generalised Hermite-Legendre orthogonal approximation are established, which plays important roles in spectral methods for various problems defined on unbounded domains. As an example, the mixed generalised Hermite-Legendre spectral scheme is constructed for anisotropic heat transfer. Its convergence is proven, and some numerical results demonstrate the spectral accuracy of this approach.