Some iterative methods for solving nonlinear equations using homotopy perturbation method

Abstract

In this paper, we use a new modified homotopy perturbation method to suggest and analyse a class of iterative methods for solving nonlinear equations. This new modification of the homotopy method is quite flexible. These new methods include the two-step Newton method as a special case. We show that these new methods are of fourth-order convergent method. Several examples are given to illustrate the efficiency and robustness of these methods.

Keywords:

• homotopy method
• iterative method
• convergence
• Newton method
• coupled system of equations

2000 AMS Subject Classification :

• 65F20
• 65N99
• 65F10
• 65F50
• 65L50

Acknowledgements

The author is grateful to the referee for his/her constructive and valuable comments and suggestions. The author would like to thank Dr S. M. Junaid Zaidi, Rector, CIIT, for providing excellent research facilities.