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An analysis of the TR-BDF2 integration scheme

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Citable URI: http://hdl.handle.net/1721.1/41736

Title: An analysis of the TR-BDF2 integration scheme
Author: Dharmaraja, Sohan
Advisor: W. Gilbert Strang.
Department: Massachusetts Institute of Technology. Computation for Design and Optimization Program.
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.
Description:
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.
Includes bibliographical references (p. 75-76).
URI: http://hdl.handle.net/1721.1/41736
Issue Date: 2007
Publisher: Massachusetts Institute of Technology
Keywords: Computation for Design and Optimization Program.

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