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Eighth Mississippi State - UAB Conference on Differential Equations & Computational Simulations
May 7-9, 2009
Department of Mathematics and Statistics, Mississippi State University
Mississippi State, MS, USA

Organizers
Mississippi State University & University of Alabama - Birmingham

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Bifurcation onto an affine subspace for separable parameterized equations
by
Yun-Qiu Shen
Western Washington University
Coauthors: Tjalling J. Ypma (Western Washington University)

Many applications give rise to separable parameterized equations of the form A(y, m)z+b(y, m)=0, where y ∈ Rn, z ∈ RN, and m ∈ R; here A(y, m) is an (N+n) ×N matrix and b(y, m) ∈ RN+n. Bifurcation onto an affine subspace occurs when A(y, m) is rank deficient at a solution of this equation. By extending a variant of the Golub-Pereyra variable projection method we derive a numerical method for computing such a point. Our method locates the bifurcation phenomenon in a smaller space than the original problem. The dimension of the problem can thus be dramatically reduced when N is much larger than n, as occurs in discretizations of differential equations. Numerical examples illustrating our method are provided.

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Date received: March 27, 2009

Copyright © 2009 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 # caxp-80.