Iterative parameter identification methods for nonlinear functions

Iterative Methods for Linear and Nonlinear Equations

Iterative Methods for Nonlinear Elliptic Equations

‖f(u)− f(v)‖−1 ≤ L‖u− v‖−1. We drop the dependence of f on x to emphasis the nonlinearity in u. Let Vh ⊂ H 0 (Ω) be the linear finite element space associated to a quasi-uniform mesh Th. The nonlinear Garlerkin method is: find uh ∈ Vh such that (2) Auh = f(uh) in Vh, where A : H 0 (Ω)→ H−1(Ω) is the elliptic operator defined by −∆. We shall assume the existence and locally uniqueness of the sol...

A one-parameter fourth-order family of iterative methods for nonlinear equations

In this paper, we present a new one-parameter fourth-order family of iterative methods for solving nonlinear equations. The new family requires two evaluations of the given function and one of its first derivative per iteration. The well-known Traub–Ostrowski’s fourth-order method is shown to be part of the family. Several numerical examples are given to illustrate the efficiency and performanc...

Latus: A new accelerator for generating combined iterative methods in solving nonlinear equation

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.