A family of fast derivative-free fourth-order multipoint optimal methods for nonlinear equations

Abstract

A new optimal family of fast derivative-free fourth-order multipoint methods for solving nonlinear equations are developed along with their convergence and computational properties. Numerical experiments in comparison with existing methods are presented to convince the theoretical development.

Keywords:

• fourth-order convergence
• optimal order
• asymptotic error constant
• efficiency index
• derivative-free

2000 AMS Subject Classifications:

• 65H05
• 65H99