Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method
Physical Review E, 2003•APS
An exact solution of the time-dependent diffusion equation for the case of a two-and a three-
layered finite diffusive medium is proposed. The method is based on the decomposition of
the fluence rate in a series of eigenfunctions and upon the solution of the consequent
transcendental equation for the eigenvalues obtained from the boundary conditions.
Comparisons among the solution of the diffusion equation and the results of Monte Carlo
simulations show the correctness of the proposed model.
layered finite diffusive medium is proposed. The method is based on the decomposition of
the fluence rate in a series of eigenfunctions and upon the solution of the consequent
transcendental equation for the eigenvalues obtained from the boundary conditions.
Comparisons among the solution of the diffusion equation and the results of Monte Carlo
simulations show the correctness of the proposed model.
Abstract
An exact solution of the time-dependent diffusion equation for the case of a two-and a three-layered finite diffusive medium is proposed. The method is based on the decomposition of the fluence rate in a series of eigenfunctions and upon the solution of the consequent transcendental equation for the eigenvalues obtained from the boundary conditions. Comparisons among the solution of the diffusion equation and the results of Monte Carlo simulations show the correctness of the proposed model.
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