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.
Highlights
Introduction and Mathematical ModelIn this note, we focus on solving pentadiagonal (PD) and tridiagonal (TD) systems of linear algebraic equations (SLEs) which are obtained after the discretization of parabolic nonlinear partial differential equations (PDEs), using finite difference methods (FDM) of second-order approximation
We focus on solving pentadiagonal (PD) and tridiagonal (TD) systems of linear algebraic equations (SLEs) which are obtained after the discretization of parabolic nonlinear partial differential equations (PDEs), using finite difference methods (FDM) of second-order approximation
A diagonal dominantization procedure was suggested. This approach ensures the stability of the suggested methods
Summary
We focus on solving pentadiagonal (PD) and tridiagonal (TD) systems of linear algebraic equations (SLEs) which are obtained after the discretization of parabolic nonlinear partial differential equations (PDEs), using finite difference methods (FDM) of second-order approximation. Such a problem was solved in [1]. There, a finite difference scheme of first-order approximation was built that leads to a TD SLE with a diagonally dominant coefficient matrix. The system was solved using the Thomas method ([2]).
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