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Absolute Stability of an Integration Method

Housam Binous
Organization: KFUPM
Department: Chemical Engineering
URL: http://sites.google.com/site/homepageofdrhousambinous/
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The notebook plots figure 4.11, page 189 of the book by Kenneth J. Beers, Numerical Methods for Chemical Engineering, Applications in Matlab, Cambridge University Press, 2007. In this figure, the magnitude of the growth coefficient vs. real and imaginary parts of the dimensionless time step is plotted. It is found that this magnitude is always less than one for the Crank-Nicholson and Implicit Euler methods of integration while it can become less than one for the Explicit Euler method. Thus, the Crank-Nicholson and Implicit Euler method are absolutely stable. We use the new features of Mathematica 6.0 (ContourLabels and RegionPlot) to display regions where the magnitude of the growth coefficient is less than one.

*Applied Mathematics
*Applied Mathematics > Numerical Methods
*Engineering > Chemical Engineering

Crank-Nicholson, Explicit Euler, Implicit Euler, Contour Plot, ContourLabels, RegionPlot, integration methods
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beers189v6.nb (483.5 KB) - Mathematica Notebook [for Mathematica 6.0]