A Family of Fifth and Sixth Convergence Order Methods for Nonlinear Models

A family of optimal iterative methods with fifth and tenth order convergence for solving nonlinear equations

In this paper, we propose a two-step method with fifth-order convergence and a family of optimal three-step method with tenth-order convergence for finding the simple roots of nonlinear equations. The optimal efficiency indices are all found to be 5 1 3 ≈ 1.71 and 10 1 4 ≈ 1.78. Some numerical examples illustrate that the algorithms are more efficient and performs better than other methods.

Some Fifth and Sixth Order Iterative Methods for Solving Nonlinear Equations

In this paper, we derive multipoint iterative methods of fifth and sixth order for finding simple zeros of nonlinear equations. The methods are based on the composition of two steps – the first step consists of Jarratt fourth order method and the second is weighted Newton step to which correction term is applied. Per iteration each method requires two evaluations of the given function and two e...

A SIXTH ORDER METHOD FOR SOLVING NONLINEAR EQUATIONS

In this paper, we present a new iterative method with order of convergence eighth for solving nonlinear equations. Periteration this method requires three evaluations of the function and one evaluation of its first derivative. A general error analysis providing the eighth order of convergence is given. Several numerical examples are given to illustrate the efficiency and performance of the new ...

An Iterative Method with Fifth-Order Convergence for Nonlinear Equations

In this paper, we suggest and analyze a new four-step iterative method for solving nonlinear equations involving only first derivative of the function using a new decomposition technique which is due to Noor [11] and Noor and Noor [16]. We show that this new iterative method has fifth-order of convergence. Several numerical examples are given to illustrate the efficiency and performance of the ...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence