Stable high-order iterative methods for solving nonlinear models

New iterative methods with seventh-order convergence for solving nonlinear equations

In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.

Fifth-order iterative methods for solving nonlinear equations

In this paper, we suggest and analyze a new two-step iterative method for solving nonlinear equation f(x) = 0 by rewriting the given nonlinear equation as a coupled system of equations and using the Taylor series. It is shown that this new iterative method is of fifth-order. Several examples are given to illustrate its performance and efficiency. Comparison with other methods is also given. Thi...

New eighth-order iterative methods for solving nonlinear equations

In this paper, three new families of eighth-order iterative methods for solving simple roots of nonlinear equations are developed by using weight function methods. Per iteration these iterative methods require three evaluations of the function and one evaluation of the first derivative. This implies that the efficiency index of the developed methods is 1.682, which is optimal according to Kung ...

High - order Newton - type iterative methods with memory for solving nonlinear equations ∗

In this paper, we present a new family of two-step Newton-type iterative methods with memory for solving nonlinear equations. In order to obtain a Newton-type method with memory, we first present an optimal two-parameter fourth-order Newton-type method without memory. Then, based on the two-parameter method without memory, we present a new two-parameter Newton-type method with memory. Using two...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations