A comparative study between an integral equation approach and a finite difference formulation for heat diffusion with nonlinear boundary conditions
type: Item
instance of: scholarly article
title: A comparative study between an integral equation approach and a finite difference formulation for heat diffusion with nonlinear boundary conditions
zbMATH Open document ID: 0806.65102
DOI: 10.1016/0307-904X(94)90355-7
author: R. Villasenor
published in: Applied Mathematical Modelling
publication date: 1995-02-09T00:00:00Z
review text: This article presents a method of finding spherically symmetric solutions of a heat equation with nonlinear boundary conditions at a sphere, arising when radiation dominates convection. It reduces the problem to a nonsingular, nonlinear Volterra equation of the second kind, and solves the latter by a linear multistep procedure based on the composite formula. The accuracy is tested by a problem with linear boundary condition allowing an analytical solution. A nonlinear boundary condition with Stefan-Boltzmann law is considered and used to show the superiority of this method to the usual finite difference calculation.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 644360
zbMATH Keywords: finite difference method
zbMATH Keywords: diffusion-convection equation
zbMATH Keywords: heat equation
zbMATH Keywords: nonlinear boundary conditions
zbMATH Keywords: nonsingular, nonlinear Volterra equation of the second kind
zbMATH Keywords: linear multistep procedure
zbMATH Keywords: Stefan-Boltzmann law
reviewed by: Akira Kaneko
MaRDI profile type: Publication
cites work: Heat diffusion with time-dependent convective boundary conditions
cites work: A new application of Lagrange-Bürmann expansions. II. Application to unsteady heat conduction problems with radiation
cites work: Q5785591
cites work: Heat transfer between solids and gases under nonlinear boundary conditions
cites work: Nonlinear Heat Transfer Problem
cites work: The energy-integral method: Application to one-phase hyperbolic Stefan problems
cites work: Gauss quadrature rules for finite part integrals
cites work: A boundary integral equation method for an inverse problem related to crack detection
cites work: Linear Multistep Methods for Volterra Integral and Integro-Differential Equations
cites work: Q3968435
cites work: Q4151113
cites work: Q5678345
cites work: Q3968434
description: scientific article; zbMATH DE number 644360