Solving nonlinear equations by a derivative-free form of the King’s family with memory
- 221 Downloads
In this paper, we present an iterative three-point method with memory based on the family of King’s methods to solve nonlinear equations. This proposed method has eighth order convergence and costs only four function evaluations per iteration which supports the Kung-Traub conjecture on the optimal order of convergence. An acceleration of the convergence speed is achieved by an appropriate variation of a free parameter in each step. This self accelerator parameter is estimated using Newton’s interpolation polynomial of fourth degree. The order of convergence is increased from 8 to 12 without any extra function evaluation. Consequently, this method, possesses a high computational efficiency. Finally, a numerical comparison of the proposed method with related methods shows its effectiveness and performance in high precision computations.
KeywordsMulti-point method Nonlinear equations Method with memory R-order of convergence Kung-Traub’s conjecture
Mathematics Subject Classification65H05
- 13.Salimi, M., Lotfi, T., Sharifi, S., Siegmund, S.: Optimal newton-secant like methods without memory for solving nonlinear equations with its dynamics. Under Revision, (2015)Google Scholar
- 14.Sharifi, S. Ferrara, M. Salimi, M. Siegmund, S.: New modification of Maheshwari method with optimal eighth order of convergence for solving nonlinear equations. Under Revision, (2015)Google Scholar
- 15.Sharifi, S. Salimi, M. Siegmund, S. Lotfi, T.: A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations. Under Revision, (2015)Google Scholar