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Approximate Solutions to the Allen-Cahn Equation Using the Finite Difference Method
(Texas A&M International University, 2016-06-13)
Seeking a deeper understanding of the world has been a driving factor in Applied Mathematics. From counting and measuring physical objects to developing equations and ratios that resemble patterns in nature, mathematics ...
Numerical Simulation of the Nagumo Equation by Finite Difference Method
(Texas A&M International University, 2015-12)
The Nagumo equation is an important nonlinear reaction-diffusion equation used to model the transmission of nerve impulses. In this thesis, traveling wave solutions to the Nagumo equation are studied. A pseudo-Crank-Nicolson ...