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Analytical solution of system of non-linear reaction-diffusion equations in a thin membrane: Homotopy perturbation approach

L.Rajendran*, V.Ananthaswamy, A.Eswari

This model is comprises of a system of time-independent reaction-diffusion equations describing steady state of a chemical process that involves three species: two reactions and diffusion. The system of equations coupled with the non-linear reaction terms with mixed Dirichlet and Neumann boundary conditions.Aclosed formof an analytical expression of concentrations for the full range of enzyme activities has been derived using Homotopy Perturbation method. A simple approximate analytical expression of concentrations in terms of dimensionless parameter  is also reported. These analytical results are compared with numerical results (MATLAB Programme) and are found to be in good agreement.