Fourth-order iterative method free from second derivative for solving nonlinear equations. (English) Zbl 1262.65058

Noor, Muhammad Aslam; Khan, Waseem Asghar

Appl. Math. Sci., Ruse 6, No. 93-96, 4617-4625 (2012).

Summary: We suggest and analyze a new two-step iterative method without second derivatives for solving nonlinear equations. We prove that the modified method has a fourth-order convergence. The efficiency index of this new method is \(4^{1/3} = 1.58\). Several examples are given to illustrate the efficiency and the performance of the new method. The new two-step iterative method can be considered as an alternative to the present fourth-order convergent methods for solving nonlinear equations.

MSC:

65H10

Numerical computation of solutions to systems of equations

Keywords:

nonlinear equations; iterative method; convergence criteria; numerical examples