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An analysis of the TR-BDF2 integration scheme

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dc.contributor.advisor W. Gilbert Strang. en_US
dc.contributor.author Dharmaraja, Sohan en_US
dc.contributor.other Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US
dc.date.accessioned 2008-05-19T16:13:17Z
dc.date.available 2008-05-19T16:13:17Z
dc.date.copyright 2007 en_US
dc.date.issued 2007 en_US
dc.identifier.uri http://hdl.handle.net/1721.1/41736
dc.description Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007. en_US
dc.description Includes bibliographical references (p. 75-76). en_US
dc.description.abstract We intend to try to better our understanding of how the combined L-stable 'Trapezoidal Rule with the second order Backward Difference Formula' (TR-BDF2) integrator and the standard A-stable Trapezoidal integrator perform on systems of coupled non-linear partial differential equations (PDEs). It was originally Professor KlausJiirgen Bathe who suggested that further analysis was needed in this area. We draw attention to numerical instabilities that arise due to insufficient numerical damping from the Crank-Nicolson method (which is based on the Trapezoidal rule) and demonstrate how these problems can be rectified with the TR-BDF2 scheme. Several examples are presented, including an advection-diffusion-reaction (ADR) problem and the (chaotic) damped driven pendulum. We also briefly introduce how the ideas of splitting methods can be coupled with the TR-BDF2 scheme and applied to the ADR equation to take advantage of the excellent modern day explicit techniques to solve hyperbolic equations. en_US
dc.description.statementofresponsibility by Sohan Dharmaraja. en_US
dc.format.extent 76 leaves en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri http://dspace.mit.edu/handle/1721.1/7582 en_US
dc.subject Computation for Design and Optimization Program. en_US
dc.title An analysis of the TR-BDF2 integration scheme en_US
dc.title.alternative Analysis of the Trapezoidal Rule with the second order Backward Difference Formula integration scheme en_US
dc.type Thesis en_US
dc.description.degree S.M. en_US
dc.contributor.department Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US
dc.identifier.oclc 225094125 en_US


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