J.-H. Jung and W. S. Don, “Collocation Methods for Hyperbolic Partial Differential Equations with Singular Sources,” The Advances in Applied Mathematics and Mechanics, Vol. 1, No. 6, 2009, pp. 769-780.

has been cited by the following article:

• TITLE: Spectral and Finite Difference Solutions of the Hyperbolic Heat Transport Equation for Thermoelectric Thin Films

  AUTHORS: Aldo Figueroa, Federico Vázquez

  KEYWORDS: Thermoelectric Cooling; Ballistic Regime; Spectral Chebyshev Collocation Method

  JOURNAL NAME: Applied Mathematics, Vol.4 No.10C, October 8, 2013

  ABSTRACT: This paper presents the numerical comparison in the solution of the hyperbolic transport Equation that models the heat flux in thermoelectric materials at nanometric length scales when the wave propagation of heat dominates the diffusive transport described by Fourier’s law. The widely used standard finite difference method fails in well-reproducing some of the physics presented in such systems at that length scale level. As an alternative, the spectral methods assure a well representation of wave behavior of heat given their spectral convergence.