All Real Roots of a Nonlinear System of Equations

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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

[more]

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.

[less]

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


Snapshots


Details

Reference

[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.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send