All Real Roots of a Nonlinear System of Equations

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Consider the system of nonlinear algebraic equations: and , where you can vary and .


This Demonstration finds all roots of this system in the domain using Seader's approach [1] and the arc length continuation technique.

The problem considered is described as follows: (the function was first proposed in [1]), , and (i.e., the auxiliary equation). Using the built-in Mathematica function WhenEvent all roots of the system are readily obtained when . A list of all roots is provided.


Contributed by: Housam Binous, Ahmed Bellagi, and Brian G. Higgins (December 2013)
Open content licensed under CC BY-NC-SA




[1] S. K. Rahimian, F. Jalali, J. D. Seader, and R. E. White, "A New Homotopy for Seeking all Real Roots of a Nonlinear Equation," Computers and Chemical Engineering, 35(3), 2011 pp. 403–411. doi:10.1016/j.compchemeng.2010.04.007.

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