A family of improved Jarratt multipoint methods

Abstract

We derive a one-parameter family of sixth-order methods for solving equations which is based on the Jarratt fourth-order multipoint method. Further, we show that a particular choice of the parameter results in fifth-order convergence. Each member of the family requires two evaluations of the given function and two of its derivative per iteration. Numerical examples are presented and the performance is compared with the Jarratt method.

Keywords:

• Non-linear equations
• Jarratt method
• Root-finding
• Convergence
• Function evaluations