dc.contributor.advisor |
Muir, Paul |
|
dc.creator |
Ellis, Adrian |
|
dc.date.accessioned |
2015-07-23T14:17:10Z |
|
dc.date.available |
2015-07-23T14:17:10Z |
|
dc.date.issued |
2014 |
|
dc.identifier.other |
QA379 E45 2014 |
|
dc.identifier.uri |
http://library2.smu.ca/xmlui/handle/01/26259 |
|
dc.description |
xii, 109 leaves : col. ill. ; 29 cm. |
|
dc.description |
Includes abstract. |
|
dc.description |
Includes bibliographical references (leaves 106-109). |
|
dc.description.abstract |
BVP_SOLVER II [Boisvert, Muir, Spiteri, 2013] is an efficient software package for the numerical solution of systems of boundary value ordinary differential equations. It employs discrete mono-implicit Runge-Kutta (MIRK) schemes to transform the ODEs into nonlinear systems which are solved by modified Newton iterations. Continuous MIRK interpolants then augment the discrete solutions from the nonlinear system, to obtain a continuous solution approximation across the problem domain. The code monitors solution quality through defect analysis and employs an adaptive mesh refinement strategy as a means of controlling the defect, which is the amount by which the computed solution fails to satisfy the ODEs. This thesis describes the development of new Hermite-Birkhoff interpolants and modifications to the BVP_SOLVER II software in order to implement a new defect estimation strategy called “Asymptotically Correct Maximum Defect Estimation”, based on the new interpolants. Numerical results which demonstrate the robustness and efficiency of the new strategy are presented. |
en_CA |
dc.description.provenance |
Submitted by Greg Hilliard (greg.hilliard@smu.ca) on 2015-07-23T14:17:10Z
No. of bitstreams: 1
Ellis_Adrian_MASTERS_2014.pdf: 5739797 bytes, checksum: 5602181eb0ba1fcfe154ff160ae55156 (MD5) |
en |
dc.description.provenance |
Made available in DSpace on 2015-07-23T14:17:10Z (GMT). No. of bitstreams: 1
Ellis_Adrian_MASTERS_2014.pdf: 5739797 bytes, checksum: 5602181eb0ba1fcfe154ff160ae55156 (MD5)
Previous issue date: 2014-07-14 |
en |
dc.language.iso |
en |
en_CA |
dc.publisher |
Halifax, N.S. : Saint Mary's University |
|
dc.subject.lcc |
QA379 |
|
dc.subject.lcsh |
Boundary value problems -- Computer programs |
|
dc.subject.lcsh |
Differential equations -- Numerical solutions -- Computer programs |
|
dc.subject.lcsh |
Runge-Kutta formulas |
|
dc.title |
Asymptotically correct defect control software for boundary value ordinary differential equations |
en_CA |
dc.type |
Text |
en_CA |
thesis.degree.name |
Master of Science in Applied Science |
|
thesis.degree.level |
Masters |
|
thesis.degree.discipline |
Mathematics and Computing Science |
|
thesis.degree.grantor |
Saint Mary's University (Halifax, N.S.) |
|