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ERROR ANALYSIS OF THE EXPONENTIAL EULER METHOD AND THE MATHEMATICAL MODELING OF RETINAL WAVES IN NEUROSCIENCE

by OH, JIYEON

Abstract (Summary)
The exponential Euler method is a specialized numerical method that was used in a software package called GENESIS which was created to model neurons and neuronal networks. In this thesis we provide a convergence analysis for this scheme in the context of some standard models from neuroscience. We provide several computational examples to further study the accuracy. We also briefly consider a simple model of neuronal network activity waves. There are two major parts to this dissertation. The first part concentrates on the error analysis of the exponential Euler scheme. The basic scheme is first order accurate. A second order modification is introduced. We also show how this exponential Euler method can be applied to mathematical models of neuronal networks that involve integro-differential equations. We prove a convergence theorem for this case. The second part of this dissertation focuses on the modeling of retinal waves in the visual cortex. We propose a firing rate model for amacrine cells.
Bibliographical Information:

Advisor:

School:University of Cincinnati

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:error analysis exponential euler mathematical neuroscience retinal waves amacrine cell

ISBN:

Date of Publication:01/01/2005

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