Computational moving boundary problems

Moving boundary and boundary value problems occur in many physical and engineering processes involving heat transfer and phase changes, they range from icing problems, for example the Stefan problem, to the melting of metals and plastics using lasers. This book reviews and compares some well known and some recently developed methods to solve these problems. Recent advances in the finite difference solution of linear and non-linear partial differential equations are presented and algorithmic manipulations that enhance the computational efficiency are incorporated into the overall schemes. In this new approach, the the finite difference substitutions are made into the solutions of the partial differential equation rather than classically into the partial differential equation itself. This approach can be exploited for many types of partial differential equation and they may therefore be of interest to researchers studying a wide range of applications in physical problems such as diffusion and heat transfer equations, optoelectronic paraxial wave equations, the quantum mechanical wave equations, time dependent pulse propagation, and similar WKB-derived problemsM