A system of first-order differential equations that arises in a model for the growth of microorganisms in a chemostat with Monod kinetics is studied. A new, semi-implicit numerical scheme is proposed to approximate solutions to the system. It is shown that the scheme is uniquely solvable and unconditionally stable, and further properties of the scheme are analyzed. The convergence rate of the numerical solution to the true solution of the system is given, and it is shown convergence of the numerical solutions to the true solutions is uniform over any interval [0, T ] for T > 0.
Seth Armstrong, Jianlong Han, and Sarah Duffin
Montgomery, Alexander Craig and Carlson, Braden J.
"Numerical Analysis of a Model for the Growth of Microorganisms,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 23:
1, Article 9.
Available at: https://scholar.rose-hulman.edu/rhumj/vol23/iss1/9