The Stability of a Semi-Implicit Numerical Scheme for a Competition Model Arising in Math Biology

Authors

Brennon Bauer, Southern Utah University
Amy Gifford, Southern Utah University

Abstract

We study a Lotka-Volterra competition model. By using the nondimensionalization method, we analyze the stability of the steady state solutions for this system. Also, a stable numerical scheme is proposed to verify the theoretical results of the system. Using the Principle of Mathematical Induction, we prove the unconditional stability and convergence of the numerical scheme.

Author Bio

Brennon Bauer is an undergraduate student studying actuarial mathematics at Southern Utah University. He has presented this research in conferences several times over the last two years, including the Mathematical Association of America’s Intermountain Conference and the Utah Conference for Undergraduate Research. Brennon’s primary area of interest in research is numerical analysis.

Amy Gifford is a senior at Southern Utah University. She is double-majoring in Pure Mathematics and Computer Science. Amy has presented this research at the Utah Conference for Undergraduate Research and the Mathematical Association of America’s Intermountain Conference. Her primary area of interest in mathematical research is differential equations. After graduation, Amy plans to attend graduate school to study Mathematics.

Faculty Sponsor

Jianlong Han

Recommended Citation

Bauer, Brennon and Gifford, Amy (2014) "The Stability of a Semi-Implicit Numerical Scheme for a Competition Model Arising in Math Biology," Rose-Hulman Undergraduate Mathematics Journal: Vol. 15: Iss. 2, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol15/iss2/3