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