On the one dimensional Stefan problem : with some numerical analysis

Abstract: In this thesis we present the Stefan problem with two boundary conditions, one constant and one time-dependent. This problem is a classic example of a free boundary problem in partial differential equations, with a free boundary moving in time. Some properties are being proved for the one-dimensional case and the important Stefan condition is also derived. The importance of the maximum principle, and the existence of a unique solution are being discussed. To numerically solve this problem, an analysis when the time t goes to zero is being done. The approximative solutions are shown graphically with proper error estimates.