Related papers: Third and Fourth-order iterative methods for solvi…

In this paper, we present an iterative three-point method with memory based on the family of King's methods to solve nonlinear equations. This proposed method has eighth order convergence and costs only four function evaluations per…

In this paper, we modify the Newton-Secant method with third order of convergence for finding multiple roots of nonlinear equations. Per iteration this method requires two evaluations of the function and one evaluation of its first…

The iterative problem of solving nonlinear equations is studied. A new Newton like iterative method with adjustable parameters is designed based on the dynamic system theory. In order to avoid the derivative function in the iterative…

In this paper, we present a new modified Newton method a use of Haar wavelet formula for solving non-linear equations. This new method do not require the use of the second-order derivative. It is shown that the new method has third-order of…

This article concerned with the issue of solving a nonlinear equation with the help of iterative method where no any derivative evaluation is required per iteration. Therefore, this work contributes to a new class of optimal eighth-order…

Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…

The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…

An implementation and an application of the combination of the genetic algorithm and Newton's method for solving a system of nonlinear equations is presented. The method first uses the advantage of the robustness of the genetic algorithm…

We propose an iterative finite element method for solving non-linear hydromagnetic and steady Euler's equations. Some three-dimensional computational tests are given to confirm the convergence and the high efficiency of the method.

In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…

We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…

In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…

In this paper, an idea to solve nonlinear equations is presented. During the solution of any problem with Newton's Method, it might happen that some of the unknowns satisfy the convergence criteria where the others fail. The convergence…

We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…

The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…

A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…

In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari method. Per iteration this method…

We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed quadrature rules. We prove that when a quadrature rule with…

The secant method, as an important approach for solving nonlinear equations, is introduced in nearly all numerical analysis textbooks. However, most textbooks only briefly address the Q-order of convergence of this method, with few…

We present a three-point iterative method without memory for solving nonlinear equations in one variable. The proposed method provides convergence order eight with four function evaluations per iteration. Hence, it possesses a very high…