Applied Math Seminar
Monday, January 17, 2000, 4:00pm, 120 Physics
Donald J. Estep (School of Mathematics, Georgia Institute of Technology)
Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations
Abstract:- One of the pressing problems in the analysis of reaction-diffusion
equations is obtaining accurate and reliable estimates of the error of
numerical solutions. Recently, we made significant progress using a new
approach that at the heart is computational rather than analytical. I
will describe a framework for deriving and analyzing a posteriori error
estimates, discuss practical details of the implementation of the
theory, and illustrate the error estimation using a variety of
well-known models. I will also briefly describe an application of the
theory to the class of problems that admit invariant rectangles and
discuss the preservation of invariant rectangles under discretization.
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