# Solution of parabolic free boundary problems using transmuted heat polynomials

## TL;DR

This paper introduces a numerical method for solving parabolic free boundary problems by utilizing transmutation operators to construct solution systems that generalize heat polynomials, with an implementation algorithm provided.

## Contribution

The paper presents a novel numerical approach based on transmutation operators to efficiently solve free boundary problems for parabolic equations, extending heat polynomial methods.

## Key findings

- Efficient construction of solution systems using transmutation operators.
- Generalization of heat polynomials for free boundary problems.
- Implementation algorithm demonstrated for the proposed method.

## Abstract

A numerical method for free boundary problems for the equation \[ u_{xx}-q(x)u=u_t \] is proposed. The method is based on recent results from transmutation operators theory allowing one to construct efficiently a complete system of solutions for this equation generalizing the system of heat polynomials. The corresponding implementation algorithm is presented.