Drawing Dynamical and Parameters Planes of Iterative Families and Methods

Dynamical ‎C‎ontrol of Computations Using the Family of Optimal Two-point Methods to Solve Nonlinear ‎Equations

One of the considerable discussions for solving the nonlinear equations is to find the optimal iteration, and to use a proper termination criterion which is able to obtain a high accuracy for the numerical solution. In this paper, for a certain class of the family of optimal two-point methods, we propose a new scheme based on the stochastic arithmetic to find the optimal number of iterations in...

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

Dynamics of a multipoint variant of Chebyshev-Halley's family

In this paper, a complex dynamical study of a parametric Chebyshev-Halley type family of iterative methods on quadratic polynomial is presented. The stability of the fixed points is analyzed in terms of the parameter of the family. We also calculate the critical points building their corresponding parameter planes which allow us to analyze the qualitative behaviour of this family. Moreover, we ...

Network Planning Using Iterative Improvement Methods and Heuristic Techniques

The problem of minimum-cost expansion of power transmission network is formulated as a genetic algorithm with the cost of new lines and security constraints and Kirchhoff’s Law at each bus bar included. A genetic algorithm (GA) is a search or optimization algorithm based on the mechanics of natural selection and genetics. An applied example is presented. The results from a set of tests carried ...