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

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

Bibliographic Details
Main Author: OH, JIYEON
Language:English
Published: University of Cincinnati / OhioLINK 2005
Subjects:
Mathematics
error analysis
Exponential Euler
Mathematical Neuroscience
Retinal Waves
Amacrine Cell
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=ucin1116256339
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-ucin11162563392021-08-03T06:10:28Z ERROR ANALYSIS OF THE EXPONENTIAL EULER METHOD AND THE MATHEMATICAL MODELING OF RETINAL WAVES IN NEUROSCIENCE OH, JIYEON Mathematics error analysis Exponential Euler Mathematical Neuroscience Retinal Waves Amacrine Cell 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. 2005-07-13 English text University of Cincinnati / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=ucin1116256339 http://rave.ohiolink.edu/etdc/view?acc_num=ucin1116256339 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Mathematics
error analysis
Exponential Euler
Mathematical Neuroscience
Retinal Waves
Amacrine Cell
spellingShingle Mathematics
error analysis
Exponential Euler
Mathematical Neuroscience
Retinal Waves
Amacrine Cell
OH, JIYEON
ERROR ANALYSIS OF THE EXPONENTIAL EULER METHOD AND THE MATHEMATICAL MODELING OF RETINAL WAVES IN NEUROSCIENCE
author OH, JIYEON
author_facet OH, JIYEON
author_sort OH, JIYEON
title ERROR ANALYSIS OF THE EXPONENTIAL EULER METHOD AND THE MATHEMATICAL MODELING OF RETINAL WAVES IN NEUROSCIENCE
title_short ERROR ANALYSIS OF THE EXPONENTIAL EULER METHOD AND THE MATHEMATICAL MODELING OF RETINAL WAVES IN NEUROSCIENCE
title_full ERROR ANALYSIS OF THE EXPONENTIAL EULER METHOD AND THE MATHEMATICAL MODELING OF RETINAL WAVES IN NEUROSCIENCE
title_fullStr ERROR ANALYSIS OF THE EXPONENTIAL EULER METHOD AND THE MATHEMATICAL MODELING OF RETINAL WAVES IN NEUROSCIENCE
title_full_unstemmed ERROR ANALYSIS OF THE EXPONENTIAL EULER METHOD AND THE MATHEMATICAL MODELING OF RETINAL WAVES IN NEUROSCIENCE
title_sort error analysis of the exponential euler method and the mathematical modeling of retinal waves in neuroscience
publisher University of Cincinnati / OhioLINK
publishDate 2005
url http://rave.ohiolink.edu/etdc/view?acc_num=ucin1116256339
work_keys_str_mv AT ohjiyeon erroranalysisoftheexponentialeulermethodandthemathematicalmodelingofretinalwavesinneuroscience
_version_ 1719432121149292544

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