Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

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 ap...

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Main Authors: Veneva Milena, Ayriyan Alexander
Format: Article
Language:English
Published: EDP Sciences 2018-01-01
Series:EPJ Web of Conferences
Online Access:https://doi.org/10.1051/epjconf/201817707004
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spelling doaj-473902cd07a34e5fa369ea3cfa8b0ae42021-08-02T06:36:25ZengEDP SciencesEPJ Web of Conferences2100-014X2018-01-011770700410.1051/epjconf/201817707004epjconf_ayss2018_07004Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEsVeneva MilenaAyriyan AlexanderA 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.https://doi.org/10.1051/epjconf/201817707004
collection DOAJ
language English
format Article
sources DOAJ
author Veneva Milena
Ayriyan Alexander
spellingShingle Veneva Milena
Ayriyan Alexander
Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs
EPJ Web of Conferences
author_facet Veneva Milena
Ayriyan Alexander
author_sort Veneva Milena
title Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs
title_short Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs
title_full Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs
title_fullStr Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs
title_full_unstemmed Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs
title_sort effective methods for solving band sles after parabolic nonlinear pdes
publisher EDP Sciences
series EPJ Web of Conferences
issn 2100-014X
publishDate 2018-01-01
description 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.
url https://doi.org/10.1051/epjconf/201817707004
work_keys_str_mv AT venevamilena effectivemethodsforsolvingbandslesafterparabolicnonlinearpdes
AT ayriyanalexander effectivemethodsforsolvingbandslesafterparabolicnonlinearpdes
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