A Simple Method for Tracking Turning Points in Parameter Space

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  • Higgins Brian G.
    Department of Chemical Engineering and Materials Science, College of Engineering, University of California
  • Binous Housam
    Department of Chemical Engineering, College of Engineering Sciences, King Fahd University of Petroleum and Minerals

書誌事項

公開日
2010
DOI
  • 10.1252/jcej.10we122
公開者
公益社団法人 化学工学会

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説明

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.

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