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A compact finite difference scheme for solving a three-dimensional heat transport equation in a thin film. (English) Zbl 0961.65072
A high-order accurate compact finite difference scheme for a heat transport equation in a thin film, where the thickness is at the microscale is developed. It is shown by a discrete Fourier analysis method that the scheme is unconditionally stable with respect to the initial values. Numerical results show that the solution is accurate. The method can be generalized to the case, where a higher-order compact finite difference is employed.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
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