Numerical method for the one phase 1D fractional Stefan problem supported by an artificial neural network

TL;DR

This paper introduces a novel numerical method combining a front fixing approach, numerical integration, and neural networks to solve a one-dimensional fractional Stefan problem, improving accuracy over previous methods.

Contribution

The paper presents a new numerical scheme that integrates neural networks with traditional methods to solve fractional Stefan problems more effectively.

Findings

The new method outperforms previous numerical schemes in accuracy.

The approach effectively approximates solutions compared to analytical results.

Neural networks enhance the stability and efficiency of the numerical solution.

Abstract

In this paper we present a numerical solution of a one-phase 1D fractional Stefan problem with Caputo derivative with respect to time variable. In the proposed approach, we use a front fixing method and the algorithm of numerical integration supported by an artificial neural network. In the final part, we present some examples illustrating the comparison of the new numerical scheme with its previous version and approximate analytical solution.