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

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.