scholarly journals ON MATHEMATICAL MODELLING OF METALS DISTRIBUTION IN PEAT LAYERS

2014 ◽  
Vol 19 (4) ◽  
pp. 568-588
Author(s):  
Ilmars Kangro ◽  
Harijs Kalis ◽  
Aigars Gedroics ◽  
Erika Teirumnieka ◽  
Edmunds Teirumnieks
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Finite Difference ◽  
Diffusion Coefficients ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Circulant Matrix ◽  
Elliptic Type ◽  
Difference Methods ◽  
The Mathematical Model

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.

scholarly journals The Mathematical Modeling of Metals Mass Transfer in Three Layer Peat Blocks

2015 ◽  
Vol 1 ◽  
pp. 87
Author(s):  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Edmunds Teirumnieks ◽  
Harijs Kalis
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Mathematical Models ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Difference Methods ◽  
The Mathematical Model

The mathematical model for calculation of concentration of metals for 3 layers peat blocks is developed due to solving the 3-D boundary-value problem in multilayered domain-averaging and finite difference methods are considered. As an example, mathematical models for calculation of Fe and Ca concentrations have been analyzed.

On finite-difference methods for the numerical solution of boundary-value problems

1961 ◽  
Vol 262 (1309) ◽  
pp. 219-236 ◽  
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Elliptic Type ◽  
Partial Differential ◽  
Difference Methods

We consider the application of finite-difference methods to the numerical solution of boundary-value problems. In particular we are concerned to study the feasibility and con­vergence of the difference-correction method for the solution of partial differential equations of elliptic type. These topics form the subject matter for §§ 3 to 6. The material of the first two sections is intended to serve as a preliminary for the main discussion. The topics considered here are finite difference formulae for numerical differentiation, and finite difference methods for the solution of partial differential equations.

scholarly journals Stability and Convergence of Two-Step Obrechkoff Scheme For Second-Order Two-Point Boundary Value Problem

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Olufemi Bosede ◽  
Ashiribo Wusu ◽  
Moses Akanbi
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Stability And Convergence ◽  
Point Boundary ◽  
Difference Methods ◽  
The Stability

Mathematical modeling of scientific and engineering processes often yield Boundary Value Problems (BVPs). One of the broad categories of numerical methods for solving BVPs is the finite difference methods, in which the differential equation is replaced by a set of difference equations which are solved by direct or iterative methods. In this paper, we use some properties of matrices to analyze the stability and convergence of the prominent finite difference methods - two-step Obrechkoff method - for solving the boundary value problem $u^{\prime \prime} = f(t,u)$, $a < x < b$, $u(a) = \eta_1$, $u(b) = \eta_2$. Conditions for the stability and convergence of the two-step Obrechkoff method method were established.

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