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An Example Showing the Peculiar Behavior of FindRoot

Housam Binous
Organization: KFUPM
Department: Chemical Engineering
URL: http://sites.google.com/site/homepageofdrhousambinous/
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When FindRoot uses Newton’s method, it may give unexpected solutions. In Fact, -f[x]/f'[x] can present sharp variations that lead FindRoot to find solutions quite far from the initial guess and different from the solutions near the initial guess. In the present notebook, we plot the solution obtained with FindRoot of a nonlinear algebraic equation versus the initial guess. We show two examples where FindRoot exhibits this peculiar behavior. This illustration of the resolution of a nonlinear algebraic equation using Newton's method was given by Kenneth J. Beers in Numerical Methods for Chemical Engineering, Applications in Matlab, Cambridge University Press, 2007.

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

FindRoot, Newton's method, initial guess, nonlinear algebraic equation
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newton_peculiar.nb (235.5 KB) - Mathematica Notebook [for Mathematica 5.2]