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A Simple Method for Tracking Turning Points in Parameter Space

Housam Binous
Organization: KFUPM
Department: Chemical Engineering
URL: http://sites.google.com/site/homepageofdrhousambinous/
Brian G. Higgins
Organization: University of California, Davis
Department: Department of Chemical Engineering & Materials Science
Revision date


We describe a simple method for tracking solutions of nonlinear equations f(u,α)=0 through turning points (also known as limit or saddle-node bifurcation points). Our implementation makes use of symbolic software such as Mathematica to derive an exact system of nonlinear ODE equations to follow the solution path, using a parameterization closely related to arc length.We illustrate our method with examples taken from the engineering literature, including examples that involve nonlinear boundary value problems that have been discretized by finite difference methods. Since the code requirement to implement the method is modest, we believe the method is ideal for demonstrating continuation methods in the classroom.

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

Nonlinear Equations, Continuation Methods, Turning Points

Binous_Higgins_2010.pdf (694.2 KB) - PDF Document