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Finite Elements and Practical Error Analysis of Huxley and EFK Equations

by Attanayake, Champike

Abstract (Summary)
In this dissertation, long time error estimates are obtained using non-traditional methods for the Hodgkin-Huxley equation ut + uxx = u(1-u)(u-a) for a ? (0,1/2) ut + ? u xxxx - uxx = u-u^3 Traditional methods for analyzing exact error propagation depends on the stability of the numerical method employed. Whereas, in this dissertation the analysis of the exact error propagation uses evolving attractors and only depends on the stability of the dynamical system. The use of the smoothing indicator yields a posteriori estimates on the numerical error instead of a priori estimates.
Bibliographical Information:

Advisor:

School:Bowling Green State University

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:finite element error huxley efk

ISBN:

Date of Publication:01/01/2008

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