Harijs Kalis, Sergejs Rogovs, Aigars Gedroics
Faculty of Physics and Mathematics
University of Latvia
8, Zellu iela, Riga, LV 1002, LATVIA

Abstract. In this paper a 2-D stationary boundary value-problem for the diffusion equation with piecewise constant coefficients in a multi-layered domain is considered. Homogeneous boundary conditions of the first kind (BC) or periodic boundary conditions (PBC) are considered in the direction. An analytical method for solving the problem of the above type is developed. This method is compared with the averaging (AV) method (using integral parabolic splines) and finite difference methods (using second-order finite difference schemes (FDS) for the space discretization in the direction) and the finite difference scheme with exact spectrum (FDSES).

Received: March 3, 2012

AMS Subject Classification: 65F15, 65L10, 65M06, 65M20, 65M22, 65M70

Key Words and Phrases: finite differences, stationary boundary-value-problem, diffusion equation, spectral problem

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