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An analysis of the TR-BDF2 integration scheme / Analysis of the Trapezoidal Rule with the second order Backward Difference Formula integration scheme

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007. / Includes bibliographical references (p. 75-76). / 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. / by Sohan Dharmaraja. / S.M.

Identiferoai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/41736
Date January 2007
CreatorsDharmaraja, Sohan
ContributorsW. Gilbert Strang., Massachusetts Institute of Technology. Computation for Design and Optimization Program., Massachusetts Institute of Technology. Computation for Design and Optimization Program.
PublisherMassachusetts Institute of Technology
Source SetsM.I.T. Theses and Dissertation
LanguageEnglish
Detected LanguageEnglish
TypeThesis
Format76 leaves, application/pdf
RightsM.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., http://dspace.mit.edu/handle/1721.1/7582

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