New iterative method for solving non-linear equations with fourth-order convergence

Abstract

In this work, we introduce an extension of the classical Newton's method for solving non-linear equations. This method is free from second derivative. Similar to Newton's method, the proposed method will only require function and first derivative evaluations. The order of convergence of the introduced method for a simple root is four. Numerical results show that the new method can be of practical interest.

Keywords:

• Newton's method
• Halley's approximation
• non-linear equation
• fourth-order convergence
• iterative method

2000 AMS Subject Classification :

• 47J05
• 41A25
• 65H05

Acknowledgements

The authors would like to thank both anonymous referees and the subject editor for their valuable comments and suggestions.