Finite Elements and Practical Error Analysis of Huxley and EFK Equations
Date of Award
Doctor of Philosophy (Ph.D.)
Mathematics/Applied Math and Scientific Computation
Tong Sun (Advisor)
So-Hsiang Chou (Committee Member)
Steven Seubert (Committee Member)
Hassan Rajaei (Committee Member)
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.
Attanayake, Champike, "Finite Elements and Practical Error Analysis of Huxley and EFK Equations" (2008). Mathematics Ph.D. Dissertations. 52.