On a Boundary Updating Method for the Scalar Stefan Problem

TL;DR

This paper introduces a versatile boundary updating method for the scalar Stefan problem, providing a theoretical foundation and demonstrating its effectiveness through computational experiments.

Contribution

It proposes a novel, general-purpose numerical method for the scalar Stefan problem, extending existing boundary updating techniques with theoretical validation.

Findings

Method successfully solves various Stefan problems.

Theoretical justification supports the method's validity.

Computational results confirm effectiveness across different scenarios.

Abstract

We report on a general purpose method for the scalar Stefan problem inspired by the standard boundary updating method used in several existence proofs. By suitably modifying it we can solve numerically any kind of Stefan problem. We present a theoretical justification of the method and several computational results.