In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in multilayered domain. We consider the metals Fe and Ca concentration in the layered peat blocks. Using experimental data the mathematical model for calculation of concentration of metals in different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations (PDEs) of second order with piece-wise diffusion coefficients in the layered domain. We develop here a finite-difference method for solving of a problem of one, two and three peat blocks with periodical boundary condition in x direction. This procedure allows to reduce the 3-D problem to a system of 2-D problems by using circulant matrix.
Kangro, I., Kalis, H., Gedroics, A., Teirumnieka, E., & Teirumnieks, E. (2014). On Mathematical Modelling of Metals Distribution in Peat Layers. Mathematical Modelling and Analysis, 19(4), 568-588. https://doi.org/10.3846/13926292.2014.963718
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