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In this study, we consider a system of degenerate reaction-diffusion equations, which govern the electric activity in the heart with a diffusion term modeling the potential in the surrounding tissue and the nonlinear ionic model proposed by Morris & Lecar. The global existence of a solution is established based on regularization argument using Fedo-Galerkin/Compactness approach. The uniqueness of the solution is shown based on Gronwell's Lemma upon some special treatment of nonlinear terms. The system of the continuous space-time model is first reduced to a semidiscrete time-dependent system based on finite element formulation, and then the fully discrete system is derived using the Backward Euler time stepping scheme. The numerical solution obtained using FreeFem++ are presented.

In this work we propose the Haar wavelet method for the coupled degenerate reaction diffusion PDEs and the ODEs having non-linear 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.

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