Analytical solutions for the non-linear differential equations in kinetic modelling of fermentative hydrogen production using new Homotopy perturbation method

Abstract

The mathematical model of fermentative hydrogen (H2) production for the hyperthermophilic marine bacterium Thermotoga neapolitana using glucose as the substrate is discussed. In this paper, new Homotopy perturbation method (iteration scheme) is employed to solve the nonlinear differential equations that describe the substrate consumption, biomass formation and hydrogen production with respect to time. The method is found to be easily implemented, fast, and computationally economical and attractive. Approximate analytical expressions for the concentrations of substrate, biomass and hydrogen are derived for various values of the kinetic parameters. The analytical results are compared with experimental data. In addition, the sensitivity of the kinetic parameters is also analyzed.