Special Splines of Exponential Type for the Solutions of Mass Transfer Problems in Multilayer Domains

    Andris Buikis Info
    Harijs Kalis Info
    Ilmars Kangro Info

Abstract

We consider averaging methods for solving the 3-D boundary-value problem of second order in multilayer domain. The special hyperbolic and exponential type splines, with middle integral values of piece-wise smooth function interpolation are considered. With the help of these splines the problems of mathematical physics in 3-D with piece-wise coefficients are reduced with respect to one coordinate to 2-D problems. This procedure also allows to reduce the 2-D problems to 1-D problems and the solution of the approximated problemsa can be obtained analytically. In the case of constant piece-wise coefficients we obtain the exact discrete approximation of a steady-state 1-D boundary-value problem.

The solution of corresponding averaged 3-D initial-boundary value problem is also obtained numerically, using the discretization in space with the central diferences. The approximation of the 3-D nonstationary problem is based on the implicit finite-difference and alternating direction (ADI) methods. The numerical solution is compared with the analytical solution.

Keywords:

special splines, averaging method, 3D problem, ADI method, analytical solution

How to Cite

Buikis, A., Kalis, H., & Kangro, I. (2016). Special Splines of Exponential Type for the Solutions of Mass Transfer Problems in Multilayer Domains. Mathematical Modelling and Analysis, 21(4), 450-465. https://doi.org/10.3846/13926292.2016.1182594

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June 23, 2016
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2016-06-23

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Review Papers

How to Cite

Buikis, A., Kalis, H., & Kangro, I. (2016). Special Splines of Exponential Type for the Solutions of Mass Transfer Problems in Multilayer Domains. Mathematical Modelling and Analysis, 21(4), 450-465. https://doi.org/10.3846/13926292.2016.1182594

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