Mathematics Ph.D. Dissertations
Finite Elements and Practical Error Analysis of Huxley and EFK Equations
Date of Award
2008
Document Type
Dissertation
Degree Name
Doctor of Philosophy (Ph.D.)
Department
Mathematics/Applied Math and Scientific Computation
First Advisor
Tong Sun (Advisor)
Second Advisor
So-Hsiang Chou (Committee Member)
Third Advisor
Steven Seubert (Committee Member)
Fourth Advisor
Hassan Rajaei (Committee Member)
Abstract
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 + γ u xxxx - uxx = u-u3
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.
Recommended Citation
Attanayake, Champike, "Finite Elements and Practical Error Analysis of Huxley and EFK Equations" (2008). Mathematics Ph.D. Dissertations. 52.
https://scholarworks.bgsu.edu/math_diss/52