A triparametric family of three-step optimal eighth-order methods for solving nonlinear equations

Abstract

A new triparametric family of three-step optimal eighth-order iterative methods free from second derivatives are proposed in this paper, to find a simple root of nonlinear equations. Convergence analysis as well as numerical experiments confirms the eighth-order convergence and asymptotic error constants.

Keywords:

• eighth-order convergence
• efficiency index
• triparametric family
• three-parameter family
• asymptotic error constant

2000 AMS Subject Classifications:

• 65H05
• 65H99