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dc.contributor.advisorFulling, Stephen A
dc.creatorThapa, Krishna 1989-
dc.date.accessioned2013-06-04T16:12:43Z
dc.date.available2013-06-04T16:12:43Z
dc.date.created2012-05
dc.date.issued2012-04-24
dc.date.submittedMay 2012
dc.identifier.urihttp://hdl.handle.net/1969.1/148831
dc.description.abstractHighly oscillatory integrals of the form $I(f)=\int_{0}^{\infty} dx f(x) e^{i \omega g(x)}$ arise in various problems in dynamics, image analysis, optics, and other fields of physics and mathematics. Conventional approximation methods for such highly oscillatory integrals tend to give huge errors as frequency ($\omega$) $\rightarrow \infty$. Over years, various attempts have been made to get over this flaw by considering alternative quadrature methods for integration. One such method was developed by Filon in 1928, which Iserles {\it et al.\ }have recently extended. Using this method, Iserles {\it et al.\ }show that as $\omega \rightarrow \infty$, the error decreases further as the error is inversely proportional to $\omega$. We use methods developed by Iserles' group, along with others like Newton-Cotes, Clenshaw-Curtis and Levin's methods with the aid of {\it Mathematica}. Our aim is to find a systematic way of calculating highly oscillatory integrals. In particular, our focus is on the oscillatory integrals that came up in earlier study of vacuum energy by Dr. Stephen Fulling.
dc.format.mimetypeapplication/pdf
dc.subjectapproximation
dc.subjectVacuum energy
dc.subjectQuadrature
dc.subjectIntegrals
dc.subjectOscillatory
dc.titleCalculating Highly Oscillatory Integrals by Quadrature Methods
dc.typeThesis
thesis.degree.departmentPhysics and Astronomy
thesis.degree.disciplinePhysics
thesis.degree.grantorHonors and Undergraduate Research
thesis.degree.nameBachelor of Science
dc.type.materialtext
dc.date.updated2013-06-04T16:12:43Z


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