Absolute Stability of an Integration Method

Shows when an integration method is absolutely stable

The program 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 superior to one for the Explicit Euler method. Thus, the Crank-Nicholson and Implicit Euler method are absolutely stable.