| Issue |
EPJ Web Conf.
Volume 177, 2018
The XXI International Scientific Conference of Young Scientists and Specialists (AYSS-2017)
|
|
|---|---|---|
| Article Number | 07004 | |
| Number of page(s) | 4 | |
| Section | Mathematical Modeling and Computational Physics | |
| DOI | https://doi.org/10.1051/epjconf/201817707004 | |
| Published online | 18 April 2018 | |
https://doi.org/10.1051/epjconf/201817707004
Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs
Joint Institute for Nuclear Research, Laboratory of Information Technologies, Joliot-Curie 6, 141980 Dubna, Moscow region, Russia
* e-mail: milena.p.veneva@gmail.com
** e-mail: ayriyan@jinr.ru
Published online: 18 April 2018
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.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.