Approximate analytical solution of non-linear reaction-diffusion equations in a cubic-autocatalytic reaction with Michaelis–Menten decay

The mathematical model pertaining to the cubic-autocatalytic reaction with M-M decay considered in one- dimensional reaction-diffusion cell is discussed. Approximate analytical solutions have been derived for the concentrations of the reactant and autocatalyst in the steady state and the non-steady state using the Homotopy analysis method. When the decay is linear, the model becomes the standard Gray-Scott model, and the corresponding approximate analytical solutions are also derived. The derived analytical expressions are compared with the numerical results with the help of MATLAB and are found to make a very good fit for small values of parameters.