A numerical method for the solution of the two-phase fractional Lame-Clapeyron-Stefan problem

TL;DR

This paper introduces a numerical method for solving a two-phase fractional Stefan problem with Caputo derivatives, employing a front-fixing approach and iterative procedure to accurately determine the moving boundary.

Contribution

It presents a novel numerical algorithm combining front-fixing and iterative methods for fractional Stefan problems, with validation against analytical solutions.

Findings

The numerical method accurately approximates the moving boundary.

Comparison shows good agreement with analytical solutions.

The approach effectively handles fractional derivatives in Stefan problems.

Abstract

In this paper we present a numerical solution of a two-phase fractional Stefan problem with time derivative described in the Caputo sense. In the proposed algorithm, we use a special case of front-fixing method supplemented by the iterative procedure, which allows us to determine the position of the moving boundary. In the final part, we also present some examples illustrating the comparison of the analytical solution with the results received by the proposed numerical method.