Date of Award
5-2025
Degree Type
Honors College Thesis
Academic Program
Mathematics BS
Department
Mathematics
First Advisor
Qingguang Guan, Ph.D.
Advisor Department
Mathematics
Abstract
ABSTRACT Hodgkin and Huxley’s nonlinear partial differential equations model the excitation and propagation of action potentials in neurons, and there have been numerous attempts at finding the best numerical solution method. This thesis proposes a novel approach to solving these equations: the Sliding Window method, in which a fixed sub-interval is found through capturing the signal’s head and tail. The system is then solved on the sub-interval instead of the entire interval. Using the Sliding Window technique also involves implementing the backward and forward Euler methods and the finite difference method. It will be demonstrated that, in utilizing the Sliding Window approach as opposed to more traditional numerical methods, we can maintain accuracy while reducing computational cost.
Copyright
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Recommended Citation
Reed, Hayden, "Sliding Window Method for Simulating Action Potentials in Axons" (2025). Honors Theses. 1004.
https://aquila.usm.edu/honors_theses/1004