Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure

High order quadrature based iterative method for approximating the solution of nonlinear equations

In this paper, weight function and composition technique is utilized to speeds up the convergence order and increase the efficiency of an existing quadrature based iterative method. This results in the proposition of its improved form from a two-point quadrature based method of convergence order ρ = 3 with efficiency index EI = 1:3161 to a three-point method of convergence order ρ = 8 with EI =...

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.    

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.

Adaptive Neural Network Method for Consensus Tracking of High-Order Mimo Nonlinear Multi-Agent Systems

This paper is concerned with the consensus tracking problem of high order MIMO nonlinear multi-agent systems. The agents must follow a leader node in presence of unknown dynamics and uncertain external disturbances. The communication network topology of agents is assumed to be a fixed undirected graph. A distributed adaptive control method is proposed to solve the consensus problem utilizing re...

Numerical Solution of Sawada-Kotera equation by using Iterative Methods