In the present chapter, the principles of the boundary element methods for
phase change problems over domains with moving boundaries are developed in
brief details. The details are developed starting from the 1-D diffusion problems
over domains with fixed boundaries subjected to different types of boundary and
initial conditions. In these problems, a new criterion has appeared: the existence of
the moving boundary, which requires special treatment when solving overall
Keywords: Boundary elements methods, moving boundary problems, Stefan condition.