An Efficient Computational Iterative Technique for a Class of Reaction-diffusion Equation

An efficient iterative method is proposed for a class of reaction-diffusion models that lead to a well-known Lane-Emden boundary value problem. Numerical investigations have been documented for two reaction-diffusion models: a spherical catalyst and a spherical biocatalyst. The proposed iterative technique is a joint venture of the Picard’s iteration scheme and the homotopy perturbation method. Making use of the Green’s function and the Picard’s method, an equivalent recursive Fredholm integral transform is established, which further reduced to a set of integral equations with the support of the concept of homotopy. The concentration of the reactant in the catalytic pellet and effectiveness factors for different values of the parameters are calculated. Numerical findings are illustrated using tables and graphs and also compared with the existing method in terms of residual errors.