A Simple Method for Tracking Turning Points in Parameter Space

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概要

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• 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 Mathematicas 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 has 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.

• 2010-12-01

著者

• Higgins Brian

  Department Of Chemical Engineering And Materials Science University Of California

• BINOUS Housam

  Department of Chemical Engineering, King Fahd University Petroleum and Minerals

• Binous Housam

  Department Of Chemical Engineering King Fahd University Petroleum And Minerals

関連論文

• A Simple Method for Tracking Turning Points in Parameter Space

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