# Numerical solution of the two-phase tumour growth model with moving boundary

## TL;DR

This paper introduces a new numerical method for solving a one-dimensional two-phase tumour growth model that simplifies boundary handling and is validated against known solutions, showing consistency with existing results.

## Contribution

A novel numerical technique for two-phase tumour growth models that avoids explicit boundary tracking and is validated against analytical solutions.

## Key findings

- Method successfully solves tumour growth equations.
- Results are consistent with existing literature.
- Advantages over previous techniques demonstrated.

## Abstract

A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution is proved. The method is tested against equations with analytically known solutions, to illustrate the advantages over the existing techniques. The tumour growth model is solved using the new procedure and showed to be consistent with results available in the literature.