Abstract. 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.Keywords: 3-D boundary-value problem, averaging method, finite difference method, heavy metals Fe and Ca, peat bog.
Bogs have been formed by an accumulation of peat - a light brown-to-black organic material, built up from partial decomposition of mosses and other bryophytes, sedges, grasses, shrubs, or trees under waterlogged conditions. The total peatlands area in Latvia covers 698 918 ha or 10.7% of the entire territory. Knowledge’s of peat metals content are important for any kind of peat using. Experimental determination of metals in peat is very long and expensive work. Using experimental data mathematical model for calculation of concentrations of metals in different points for different layers can help to very easy and fast to find approximately concentration of metals or trace elements. The results of the research show that concentrations of trace elements in peat are generally low. Concentrations differ between the superficial, middle and bottom peat layers, but the significance decreases depending on the type of mire. The mathematical model for calculation of concentration of metals in different points for different 3 layers in peat blocks is developed. As an example, mathematical models for calculation of Ca and Fe concentrations have been analyzed.
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