Keywords

Reaction diffusion equation; propagation failure; discrete nagumo

Abstract

Spatially discrete Nagumo equations have widespread physical applications, including modeling electrical impulses traveling through a demyelinated axon, an environment typical in multiple scle- rosis. We construct steady-state, single front solutions by employing a piecewise linear reaction term. Using a combination of Jacobi-Operator theory and the Sherman-Morrison formula we de- rive exact solutions in the cases of homogeneous and inhomogeneous diffusion. Solutions exist only under certain conditions outlined in their construction. The range of parameter values that satisfy these conditions constitutes the interval of propagation failure, determining under what circumstances a front becomes pinned in the media. Our exact solutions represent a very specific solution to the spatially discrete Nagumo equation. For example, we only consider inhomogeneous media with one defect present. We created an original script in MATLAB which algorithmically solves more general cases of the equation, including the case for multiple defects. The algorithmic solutions are then compared to known exact solutions to determine their validity.

Notes

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Graduation Date

2015

Semester

Summer

Advisor

Moore, Brian

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematical Science

Format

application/pdf

Identifier

CFE0005831

URL

http://purl.fcla.edu/fcla/etd/CFE0005831

Language

English

Release Date

August 2018

Length of Campus-only Access

3 years

Access Status

Masters Thesis (Open Access)

Subjects

Dissertations, Academic -- Sciences; Sciences -- Dissertations, Academic

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Included in

Mathematics Commons

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