SOME OPTIMAL METHODS WITH EIGHTH-ORDER CONVERGENCE FOR THE SOLUTION OF NONLINEAR EQUATIONS

Abstract

In this paper we propose a new family of eighth order optimal methods for solving nonlinear equations by using weight function methods. The methods of the family require three function and one derivative evaluations per step and has order of convergence eight, and so they are optimal in the sense of Kung-Traub hypothesis. Precise analysis of convergence is given. Some members of the family are compared with several existing methods to show their performance and as a result to confirm that our methods are as competitive as compared to them.

This article was migrated from the previous system via automation. The abstract may not be written correctly. Please view the PDF file.