Abstract:
In this paper, we present a solution of an ice melting problem using a fixed domain method for one-dimensional diffusion equation with a moving boundary position as the time variable. These kinds of problems arise in mathematical models of several applications in Engineering, biological process, chemical diffusion and different branches of physics. We include a transformation to fix the moving boundary using a conventional finite difference technique on the unknown domain. The boundary velocity becomes a second dependent variable. This problem was solved by a modified variable time step method [1].
Key Words: Stefan problems, moving boundary problems, phase transformations, heat equation, partial differential equations, finite difference.
2010 Mathematics Subject Classification: Primary 35K05, 35R35, 35R37; Secondary 80A22, 65M06, 65N06.
