### A First Order Singular Perturbation Solution to a Simple One-Phase Stefan Problem with Finite Neumann Boundary Conditions

**Authors:** Bruce Rout

**Comments:** 13 pages

This paper examines the difference between infinite and finite domains
of a Stefan Problem. It is pointed out that attributes of solutions
to the Diffusion Equation suggest assumptions of an infinite domain
are invalid during initial times for finite domain Stefan Problems. The
paper provides a solution for initial and early times from an analytical
approach using a perturbation. This solution can then easily be applied
to numerical models for later times. The differences of the two domains
are examined and discussed.

**Category:** Mathematical Physics