Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer

TL;DR

This paper develops and analyzes a numerical method combining front fixing, finite difference, and collocation techniques to efficiently solve a complex nonlinear free boundary model of prostate tumor growth, with proven stability and convergence.

Contribution

It introduces a novel numerical approach for a coupled nonlinear prostate cancer model, with rigorous stability and convergence analysis, and demonstrates its effectiveness through numerical experiments.

Findings

The method is stable and convergent for the prostate tumor model.

Numerical results confirm the efficiency of the proposed approach.

The approach accurately captures tumor growth dynamics.

Abstract

The main target of this paper is to present an efficient method to solve a nonlinear free boundary mathematical model of prostate tumor. This model consists of two parabolics, one elliptic and one ordinary differential equations that are coupled together and describe the growth of a prostate tumor. We start our discussion by using the front fixing method to fix the free domain. Then, after employing a nonclassical finite difference and the collocation methods on this model, their stability and convergence are proved analytically. Finally, some numerical results are considered to show the efficiency of the mentioned methods.