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A family of ellipse methods for solving non-linear equations

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Abstract:

This note presents a method for the numerical approximation of simple zeros of a non-linear equation in one variable. In order to do so, the method uses an ellipse rather than a tangent approach. The main advantage of our method is that it does not fail even if the derivative of the function is either zero or very small in the vicinity of the required root.

Keywords: Newton's method; non-linear equations; order of convergence

Document Type: Research Article

DOI: https://doi.org/10.1080/00207390902825336

Affiliations: 1: Department of Applied Sciences, Indo Global College of Engineering, Mohali, Punjab, India 2: University Institute of Engineering and Technology, Panjab University, Chandigarh-160 014, India

Publication date: 2009-01-01

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