Variable-step variable-order 3-stage Hermite-Birkhoff ODEDDE solver of order 5 to 15

Variable-step variable-order 3-stage Hermite-Birkhoff ODEDDE solver of order 5 to 15

This thesis presents the variable-step variable-order 3-stage Hermite-Birkhoff numerical solver HB515DDE of order 5 to 15. This method can solve ordinary and delay differential equations (ODEs/DDEs) with state-dependent, non-vanishing, small, vanishing and asymptotically vanishing delays. Delayed va...

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Bibliographic Details
Main Author: Yagoub, Hemza
Format: Others
Language:en
Published: University of Ottawa (Canada) 2013
Subjects:
Mathematics.
Online Access:http://hdl.handle.net/10393/28075
http://dx.doi.org/10.20381/ruor-12376
id ndltd-uottawa.ca-oai-ruor.uottawa.ca-10393-28075
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spelling ndltd-uottawa.ca-oai-ruor.uottawa.ca-10393-280752018-01-05T19:07:49Z Variable-step variable-order 3-stage Hermite-Birkhoff ODEDDE solver of order 5 to 15 Yagoub, Hemza Mathematics. This thesis presents the variable-step variable-order 3-stage Hermite-Birkhoff numerical solver HB515DDE of order 5 to 15. This method can solve ordinary and delay differential equations (ODEs/DDEs) with state-dependent, non-vanishing, small, vanishing and asymptotically vanishing delays. Delayed values are computed using Hermite interpolation and small delays are dealt with using extrapolation. Discontinuities in DDEs are located by a bisection method. HB515DDE was tested and compared with other solvers. The results are given along with the convergence theory which supports the experimentation. 2013-11-07T19:03:28Z 2013-11-07T19:03:28Z 2009 2009 Thesis Source: Masters Abstracts International, Volume: 48-01, page: 0431. http://hdl.handle.net/10393/28075 http://dx.doi.org/10.20381/ruor-12376 en 77 p. University of Ottawa (Canada)
collection NDLTD
language en
format Others
sources NDLTD
topic Mathematics.
spellingShingle Mathematics.
Yagoub, Hemza
Variable-step variable-order 3-stage Hermite-Birkhoff ODEDDE solver of order 5 to 15
description This thesis presents the variable-step variable-order 3-stage Hermite-Birkhoff numerical solver HB515DDE of order 5 to 15. This method can solve ordinary and delay differential equations (ODEs/DDEs) with state-dependent, non-vanishing, small, vanishing and asymptotically vanishing delays. Delayed values are computed using Hermite interpolation and small delays are dealt with using extrapolation. Discontinuities in DDEs are located by a bisection method. HB515DDE was tested and compared with other solvers. The results are given along with the convergence theory which supports the experimentation.
author Yagoub, Hemza
author_facet Yagoub, Hemza
author_sort Yagoub, Hemza
title Variable-step variable-order 3-stage Hermite-Birkhoff ODEDDE solver of order 5 to 15
title_short Variable-step variable-order 3-stage Hermite-Birkhoff ODEDDE solver of order 5 to 15
title_full Variable-step variable-order 3-stage Hermite-Birkhoff ODEDDE solver of order 5 to 15
title_fullStr Variable-step variable-order 3-stage Hermite-Birkhoff ODEDDE solver of order 5 to 15
title_full_unstemmed Variable-step variable-order 3-stage Hermite-Birkhoff ODEDDE solver of order 5 to 15
title_sort variable-step variable-order 3-stage hermite-birkhoff odedde solver of order 5 to 15
publisher University of Ottawa (Canada)
publishDate 2013
url http://hdl.handle.net/10393/28075
http://dx.doi.org/10.20381/ruor-12376
work_keys_str_mv AT yagoubhemza variablestepvariableorder3stagehermitebirkhoffodeddesolveroforder5to15
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