Optimal low-dimensional dynamical approximations

Sirovich, L.; Knight, B. W.; Rodriguez, J. D.

doi:10.1090/qam/1074969

Authors: L. Sirovich, B. W. Knight and J. D. Rodriguez
Journal: Quart. Appl. Math. 48 (1990), 535-548
MSC: Primary 58F39; Secondary 35C99, 35Q55, 58F12, 76E30
DOI: https://doi.org/10.1090/qam/1074969
MathSciNet review: MR1074969
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Abstract: We present a method for determining optimal coordinates for the representation of an inertial manifold of a dynamical system. The condition of optimality is precisely defined and is shown to lead to a unique basis system. The method is applied to the Neumann and Dirichlet problems for the Ginzburg-Landau equation. Substantial reduction in the size of the dynamical system, without loss of accuracy is obtained from the method.

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