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Abstract

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.

Author Bio

Craig Montgomery graduated with a bachelor’s degree in Mathematics from Southern Utah University in the Spring of 2021. He is beginning a master’s program at Utah State University as of fall 2021, and plans to eventually get a Ph.D. and become a professor. This research project began in January of 2020, and the research was completed in the end of the Spring 2021 semester. Some of Craig's non-math interests include video games, board games, cubing, and Taekwondo.

Braden Carlson is planning on graduating with a bachelor’s degree in Mathematics from Southern Utah University in the spring of 2022. He then plans on attending a Graduate program in Mathematics with aspirations to become a professor. Braden enjoys programming and learning about computer architecture, as well as Chess and skiing.

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