Abstract
The phenomena of melting and solidification have many current engineering applications. For example, ground freezing problems are considered as moving boundary problems (MBP) defined in semi-infinite region. This paper presents a simple and effective numerical method for the one-dimensional MBP. By use of coordinate transformation, the semi-infinite region (0, ∞) is mapped into a finite region lying between (0, 1). To this end, we consider two mappings (an exponential map and an algebraic map). The collocation method is employed to replace a partial differential equations by a system of ordinary differential equations in time, and the resulting equations are solved by the mid-interval Crank-Nicolson algorithm. Several numerical examples are analyzed in order to show the performance of the proposed methodology.
