A mixed collocation-finite difference method for 3D microscopic heat transport problems (Q929915)

The authors consider a 3D microscopic heat transport problem where the thickness in the considered domain is much smaller than both the length and width. A spectral collocation method is proposed to discretize the 3D space while the finite difference technique is used to discretize the time. The consistency, stability and convergence analysis of the mixed collocation-fixed difference method are provided. The method is tested by a numerical example.