Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs
Incremental solution for a specific class of heat transfer problems in multilayer domains.
The paper tackles solving pentadiagonal systems from nonlinear parabolic PDEs in multilayer heat transfer, proposing diagonal dominantization and symbolic methods. No concrete results or numbers are provided.
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.