A Comparison of First- and Second Order-in-Time Finite Difference Methods Applied to Nonlinear Reactive Transport

In this paper, we consider solution methods for the nonlinear reactive transport equation used to model the protein adsorption process. Efficient methods for simulating this process are necessary to aid in the development of novel adsorptive chromatography media to ensure high-volume production of purified product for the purposes of biotherapeutics. Using MATLAB®, we compare four finite difference schemes used to solve the nonlinear reactive transport equation, focusing on the differences of efficacy between implicit and explicit methods. As such, two of the methods are semi-implicit and two are explicit with one of each kind using a first-order temporal scheme and one of each using a second-order temporal scheme. The semi-implicit methods evaluate almost all terms implicitly while lagging the nonlinear coefficient function in time to linearize the equations. We include numerical results that indicate optimal convergence of the schemes, and we compare the effectiveness of the schemes in matching experimental data using two different boundary conditions.