A Modified Eighth-Order Derivative-Free Root Solver

Fazlollah Soleymani, S. Karimi Vanani

Abstract

This paper proposes a modified technique for solving nonlinear equations. The technique is fully free from derivative calculation per full cycle and consumes only four pieces of function evaluations to reach the local convergence rate eight. This shows that our technique is optimal due to the conjecture of Kung and Traub. The contributed class is built by using weight function approach. In the sequel, theoretical results are given and finally numerical examples are employed to evaluate and illustrate the accuracy of the novel methods derived of the modified technique.