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A mixed collocation-finite difference method for 3D microscopic heat transport problems. (English) Zbl 1148.65082
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.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
Software:
Matlab
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