A Reliable Spectral Method to Reaction-Diffusion Equations in Entrapped-Cell Photobioreactor Packed with Gel Granules Using Chebyshev Wavelets.

Abstract

A mathematical model of a reaction-diffusion within an entrapped-cell photobioreactor packed with gel granules containing immobilized photosynthetic bacterial cells is discussed. A theoretical model is based on a system of coupled nonlinear reaction-diffusion equations. In this research work, we have developed an efficient wavelet-based spectral approach for solving the proposed model. Analytical expressions for the concentration of substrate and product are established for all values of reaction-diffusion parameters using second kind Chebyshev wavelet method. The analytical results were also compared with Homotopy perturbation method (HPM) and Adomian decomposition method (ADM). Satisfactory agreement with ADM and HPM solutions is observed. Moreover, the use of Chebyshev wavelets is found to be simple, reliable, efficient, and computationally attractive.