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The Additional Dynamics of Least Squares Completions for Differential Algebraic Equations
by
Irfan Okay
Department of Mathematics, North Carolina State University
Coauthors: Dr. Stephen L. Campbell,. Department of Mathematics, North Carolina State University;
Dr. Peter Kunkel, Universitšat Leipzig, Mathematisches Institut Augustusplatz
One method for numerically solving Differential Algebraic Equations (DAE) is called explicit integration (EI). The method is based on forming a derivative array by differentiating the original equation a number of times and solving that system using least squares method. When sufficient number of differentiations are taken, this leads to an ODE called the least squares completion. This ODE contains the solutions of the original DAE as well as additional solutions imposed by extra differentiations. When the ODE is integrated numerically, these additional dynamics can cause drift off the solution manifold.
Starting with linear systems ,we first determine the additional dynamics of the least squares completions, then give appropriate reformulations of the derivative array which result in a stable system.
Date received: February 27, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cauj-11.