Solving nonlinear equations from higher order derivations in linear stages

Higher-order Iterative Algorithms for Solving Nonlinear Equations

In this paper, we use the new decomposition technique to suggest and analyze new iterative methods for solving nonlinear equations. Our technique of developing these iterative methods is very simple as compared with other techniques. We prove the eighth order convergence of the proposed method. Various numerical examples are given to illustrate the performance of the new method.

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 ...

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

A Note on Some Higher-Order Iterative Methods Free from Second Derivative for Solving Nonlinear Equations

In the recent paper [M. A. Noor, W. A. Khan, K. I. Noor and Eisa Al-Said, Higher-order iterative methods free from second derivative for solving nonlinear equations, International Journal of the Physical Sciences, Vol. 6 (8) (2011), 1887-1893] several iterative methods for solving nonlinear equations are presented. One of the methods is the three-step iterative method given in Algorithm (2.10) ...

Solving higher order equations: from logic to programming

Higher order constructs provide the necessary level of abstraction for concise and natural formulations in many areas of computer science We present constructive methods for higher order equational reasoning with applications ranging from theorem proving to novel programming concepts A major problem of higher order programming is the undecidability of higher order uni cation In the rst part we ...