Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs
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Publication:6292009
DOI10.1051/EPJCONF/201817707004arXiv1710.00428MaRDI QIDQ6292009
Milena Veneva, Alexander Ayriyan
Publication date: 1 October 2017
Abstract: A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer. Homogeneous Neumann boundary conditions and ideal contact ones are applied. A finite difference scheme on a special uneven mesh with a second-order approximation in the case of a piecewise constant spatial step is built. This discretization leads to a pentadiagonal system of linear equations (SLEs) with a matrix which is neither diagonally dominant, nor positive definite. Two different methods for solving such a SLE are developed -- diagonal dominantization and symbolic algorithms.
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