Optimal equi-scaled families of Jarratt's method

Abstract

In this paper, we present many new fourth-order optimal families of Jarratt's method and Ostrowski's method for computing simple roots of nonlinear equations numerically. The proposed families of Jarratt's method having the same scaling factor of functions as that of Jarratt's method (i.e. quadratic scaling factor of functions in the numerator and denominator of the correction factor) are the main finding of this paper. It is observed that the body structures of our proposed families of Jarratt's method are simpler than those of the original families of Jarratt's method. The efficiency of these methods is tested on a number of relevant numerical problems. Furthermore, numerical examples suggest that each member of the proposed families can be competitive to other similar robust methods available in the literature.

Keywords:

• nonlinear equations
• simple roots
• Halley's method
• Schröder's method
• Jarratt's method
• Ostrowski's method
• optimal order of convergence
• efficiency index

2010 AMS Subject Classifications:

• 65H05
• 65H99

Acknowledgements

We express our gratitude to the Editor for his constructive suggestions and remarks which have considerably contributed to the readability of this paper. Ramandeep Behl further acknowledges CSIR, New Delhi, India, for the financial support.