dc.contributor.advisor |
Butcher, J. C. |
en |
dc.contributor.advisor |
Burrage, Kevin |
en |
dc.contributor.author |
Aziz, Mubin Ahmed |
en |
dc.date.accessioned |
2007-09-03T10:26:33Z |
en |
dc.date.available |
2007-09-03T10:26:33Z |
en |
dc.date.issued |
1987 |
en |
dc.identifier |
THESIS 88-064 |
en |
dc.identifier.citation |
Thesis (PhD--Computer science)--University of Auckland, 1987 |
en |
dc.identifier.uri |
http://hdl.handle.net/2292/1683 |
en |
dc.description |
Full text is available to authenticated members of The University of Auckland only. |
en |
dc.description.abstract |
This thesis is concerned with an initial value system of the form
y’(t)=f(y(t),t), y(0)=y0,
where it is known that the solution y is approximately periodic with period T. Methods are desired which take large steps compared with T but at the expense of following precise details of every cycle. The essential idea is to define a function z(t), known as a quasi-envelope which does not necessarily agree with y on (O,T), but for which y(t)=z(t), where t is an integral multiple of T. Thus
z(t+T)=z(t)+Tg(z(t),t)
where g(z,t) is found by integrating the original differential equation through an interval from t to t+T with initial value at t equal to z. Generalized Runge-Kutta methods are derived which can efficiently solve non-stiff highly oscillatory problems by using large stepsizes. Methods of this type involves two levels of computation: integration at a local level to evaluate g, and performing the large steps through which z progresses. A fixed order, fixed stepsize version of program is presented. Numerical examples shows that this method can efficiently solve several highly oscillatory problems. |
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dc.language.iso |
en |
en |
dc.publisher |
ResearchSpace@Auckland |
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dc.relation.ispartof |
PhD Thesis - University of Auckland |
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dc.relation.isreferencedby |
UoA9910696514002091 |
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dc.rights |
Restricted Item. Available to authenticated members of The University of Auckland. |
en |
dc.rights |
Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. |
en |
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
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dc.title |
Runge-Kutta methods for oscillatory problems |
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dc.type |
Thesis |
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thesis.degree.discipline |
Computer Science |
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thesis.degree.grantor |
The University of Auckland |
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thesis.degree.level |
Doctoral |
en |
thesis.degree.name |
PhD |
en |
dc.rights.holder |
Copyright: The author |
en |
dc.identifier.wikidata |
Q112845992 |
|