Solution of Nonlinear Reaction-Diffusion Model in Porous Catalysts Arising in Micro-Vessel and Soft Tissue Using a Metaheuristic

Abstract

The steady-state reactive transport model (RTM) is a generalization of the nonlinear reaction-diffusion model in porous catalysts. The RTM is expressed as a non-linear ordinary differential equation of second-order with boundary conditions. Artificial neural network (ANN), Particle swarm optimization (PSO), and hybrid of PSO-SQP (Sequential Quadratic Programming) are used to obtain accurate, approximate solutions to the non-linear RTM. The proposed technique is applied to three different cases of non-linear RTM. The properties of the nonlinear reactive transport model in porous catalysts are investigated by considering various cases based on variation in the half-saturation concentration “ $\alpha $ ” and the characteristic reaction rate “ $\beta $ .” The stability, reliability, and exactness of the proposed technique are established through comparison with the outcomes of the standard numerical procedure with the RK4 method and along with the different performance indices, which are Root-Mean-Square Error (RMSE), (TIC), Absolute Error (AE), and Mean Absolute Deviation (MAD).

Keywords

• Artificial neural networks
• nonlinear reactive transport model
• particle swarm optimization
• mathematical modeling