A comparative study between an integral equation approach and a finite difference formulation for heat diffusion with nonlinear boundary conditions
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.
nonsingular, nonlinear Volterra equation of the second kind
scientific article; zbMATH DE number 644360
scientific article