An application of the LTDRM to transient diffusion problems with nonlinear material properties and nonlinear boundary conditions
type: Item
instance of: scholarly article
title: An application of the LTDRM to transient diffusion problems with nonlinear material properties and nonlinear boundary conditions
zbMATH Open document ID: 0907.65097
DOI: 10.1016/S0096-3003(96)00226-3
author: Pornchai Satravaha
author: Song-Ping Zhu
published in: Applied Mathematics and Computation
publication date: 1999-02-18T00:00:00Z
review text: Transient diffusion problems with nonlinear material properties and a combination of Dirichlet, Neumann, convective and radiative boundary conditions are investigated. The nonlinearity of the thermal conductivity term \(K\) is as follows: \( K(u)= K_0(1+\beta u)\), where \(K_0,\;\beta\) are material dependent constants and \(u\) is a function of the unknown temperature. Two methods, with and without Kirchhoff transformation, are discussed. The nonlinear terms in both the governing equation and the boundary conditions are linearized first followed by the removal of the time variable from the linearized differential system with the Laplace transformation, and then the problem is solved by the dual reciprocity method. Two formulations of the Laplace transform dual reciprocity method (LTDRM) are derived: a formulation involving first-order spatial derivates (LPTDRM-1) and a formulation involving second-order spatial derivates (LPTDRM-2). Six examples are presented to show the efficiency and accuracy of the investigated method. These numerical solutions are compared with those obtained analytically or numerically.
reviewed by: Angela Handlovičová
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1183167
zbMATH Keywords: diffusion problems
zbMATH Keywords: nonlinear material properties
zbMATH Keywords: nonlinear boundary conditions
zbMATH Keywords: Laplace transform
zbMATH Keywords: Kirchhoff transformation
zbMATH Keywords: numerical examples
zbMATH Keywords: dual reciprocity method
describes a project that uses: Algorithm 368
MaRDI profile type: Publication
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full work available at URL: s0096-3003(96)00226-3
OpenAlex ID: W2011838386
description: scientific article; zbMATH DE number 1183167