A Numerical Method for a Stefan-Type Problem

Abstract

A Stefan-type problem is considered. This is an initial-boundary value problem on a composite domain for a parabolic reaction-diffusion equation with a moving interface boundary. At the moving boundary between the two subdomains, an interface condition is prescribed for the solution of the problem and its derivatives. A finite difference scheme is constructed that approximates the initial-boundary value problem. An iterative Newton-type method for the solution of the difference scheme and a numerical method for the analysis of the errors of the computed discrete solutions are both developed. Keywords:Stefan-type problem, initial-boundary value problem, composite domain, parabolic reaction-diffusion equation, moving interface boundary, finite difference scheme, iterative Newton-type method.