Nodal integral and finite difference solution of one-dimensional Stefan problem

The nodal integral and finite difference methods are useful in the solution of one-dimensional Stefan problems describing the melting process. However very few explicit analytical solutions are available in the literature for such problems, particularly with time-dependent boundary conditions. Benchmark cases are presented involving two test examples with the aim of producing very high accuracy when validated against the exact solutions. Test example 1 (time-independent boundary conditions) is followed by the more difficult test example 2 (time-dependent boundary conditions). As a result, the temperature distribution, position of the moving boundary and the velocity are evaluated and the results are validated.