# Haar wavelet method for the coupled degenerate reaction-diffusion PDEs and the ODEs having a non-linear source

## TL;DR

This paper introduces a Haar wavelet numerical method for solving coupled degenerate reaction-diffusion PDEs and ODEs with nonlinear sources, demonstrating convergence and applying it to medically relevant models.

## Contribution

The paper develops a Haar wavelet-based numerical scheme for complex coupled PDE-ODE systems with nonlinear sources, including convergence analysis and practical medical applications.

## Key findings

- Successfully solved model problems of medical significance.
- Demonstrated convergence of the numerical scheme.
- Used GMRES solver for efficient linear system solutions.

## Abstract

In this work, we propose the Haar wavelet method for the coupled degenerate reaction-diffusion PDEs and the ODEs having non-linear a source with Neumann boundary, applicable in various fields of the natural sciences, engineering, and economics, for example in gas dynamics, certain biological models, assets pricing in economics, composite media etc. Convergence analysis of the proposed numerical scheme has been carried out. We use the GMRES solver to solve the linear system of equations. Numerical solutions for the model problems of medical significance have been successfully solved.