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About 10,000 papers for “Iterative Methods for Nonlinear Equations”

Iterative Methods For Solving Nonlinear Lane-Emden Equations]{Iterative Methods For Solving Nonlinear Lane-Emden Equations

Faruk Uçar, Volkan Yaman, Bülent Yılmaz · Marmara Fen Bilimleri Dergisi · 2018

In this paper we derive solutions for the nonlinear Lane-Emden type of equations with iterative methods, Daftardar-Jafari Method (DJM), Adomian Decomposition Method (ADM) and Differential Transform Method (DTM). The difficulty of Lane-Emden type of equations for implementing these iterative methods is due to the singularity at $x = 0$. We compare the efficiency of DJM - which is the authentic part of the paper - with ADM and DTM in solving the nonlinear, singular, initial value Lane-Emden type of equations.

Cited by 1Open access

Iterative Methods For Solving Nonlinear Lane-Emden Equations]{Iterative Methods For Solving Nonlinear Lane-Emden Equations

Dspace Repository (Marmara Üniversitesi) · 2022

In this paper we derive solutions for the nonlinear Lane-Emden type of equations with iterative methods, Daftardar-Jafari Method (DJM),Adomian Decomposition Method (ADM) and Differential Transformation Method (DTM). The difficulty of Lane-Emden type of equationsfor implementing these iterative methods is due to the singularity at. We compare the efficiency of DJM – which is the authenticpart of the paper – with ADM and DTM in solving the nonlinear, singular, initial value Lane-Emden type of equations.

Cited by 0Open access

Iterative Methods for Linear and Nonlinear Equations

C. T. Kelley · Society for Industrial and Applied Mathematics eBooks · 1995

No wananties, express or implied, are made by the publisher, aathors and their employers that the programs eontained in this volmoe are free of error.They s~ouidnotbe ndied on as the sole basis to solve a problem whose incorrect solution conld result in injury to person or property.Ifthepeograimsareemployedinsuchamanner,itisattheuser's ownriskandtbepublisher, author, and their employers disclaim all liability for such misuse.

Cited by 1,582Open access

ITERATIVE SELF-LEARNING METHODS FOR SOLVING NONLINEAR EQUATIONS

Y. S Popkov · Автоматика и телемеханика · 2024

Рассматривается задача решения системы нелинейных уравнений с произвольной, но непрерывной вектор-функцией в левой части, о которой можно иметь только значения ее компонент. Для определения приближенного решения используется какой-нибудь итерационный метод с параметрами, качественные свойства которого оцениваются квадратичным функционалом невязки. Предлагается самообучающаяся процедура (подкрепления), основанная на вспомогательных МК-испытаниях, на функции полезности экспоненциального класса и функции выигрыша, реализующей принцип оптимальности Беллмана. Доказана теорема о строгом монотонном убывании функционала невязки.

Cited by 0Open access

Higher-Order Iterative Methods for Solving Nonlinear Equations

I. A. Al-Subaihi · 2014

In this report, we presented three high-order iterative methods for solving nonlinear equations of the form 0 = ) (x f . These proposed iterative methods are obtained by combining a fourth-order iterative method with the classical Newton's method and approximating the first derivative in the third step by three different approaches of combinations of previously evaluated function values. The convergence analyses of the new methods are discussed, and several examples are given to illustrate the methods' efficiency. (Al-Subaihi IA., Al-qarni AJ. Higher-Order Iterative Methods for Solving Nonlinear Equations. Life Sci J 2014;11(12):85-91). (ISSN:1097-8135). http://www.lifesciencesite.com . 15

Cited by 7

Iterative Methods for Finding Roots of Nonlinear Equations

Mohammed Rasheed, Suha SHIHAB, Ahmed Rashid et al. · Journal of Al-Qadisiyah for Computer Science and Mathematics · 2021

In the present work, two iterative techniques have been displayed in order to solve non-linear equation. These two techniques are free from second derivative and per evaluation; they require five and six iterations with a first derivative of the function. Analysis of the PV model has been studied in term of function evaluations appears that the proposed technique is superior. It is practical interest is investigated by some numerical examples.

Cited by 20Open access

On some iterative methods for solving nonlinear equations

Emil Cătinaş · SHILAP Revista de lepidopterología · 1994

Let \(h(x):=f(x)+g(x)=0\), with \(f\) differentiable and \(g\) continuous, where \(f,g,h:X \rightarrow X\), \(X\) a Banach space. The Newton method cannot be applied for solving \(h(x)=0\), and we propose an iterative method for solving the nonlinear equation, by combining the Newton method (for the differentiable part) with the chord/secant method (for the nondifferentiable part): \[x_{k+1} = \big(f^\prime(x_k)+[x_{k-1},x_k;g]\big)^{-1}(f(x_k)+g(x_k)).\] We show that the r-convergence order of the method is the same as of the chord/secant method. We provide some numerical examples and compare different methods for a nonlinear system in \(\mathbb{R}^2\). [Editor note: for a series of papers dealing with the notion of convergence orders, see the convergence orders category]

Cited by 3Open access

New iterative methods for nonlinear equations in R

Sukhjit Singh, Divyansh Gupta · International Journal of Mathematics in Operational Research · 2016

A parameter based on two-step iterative method combining two known third order methods is proposed for solving nonlinear equations in R. The convergence analysis of the method is established to show its fourth order of convergence. In order to enhance the order of convergence from four to seven, its three-step extension is also developed. The increase in the number of function evaluations is reduced by approximating the involved derivative in the third step by the second order divided differences. A number of numerical examples are worked out to demonstrate the efficacy of both the methods. The performance measures used are the number of iterations and the total number of function evaluations required to get an approximation to the root correct up to fifteen decimal places. The informational index and efficiency index of the proposed methods are computed. On comparison with the existing methods, it is observed that our methods give improved performance in terms of computational speed and efficiency.

Cited by 1

Scalable nonlinear iterative methods for partial differential equations

X-C Cai · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2000

We conducted a six-month investigation of the design, analysis, and software implementation of a class of singularity-insensitive, scalable, parallel nonlinear iterative methods for the numerical solution of nonlinear partial differential equations. The solutions of nonlinear PDEs are often nonsmooth and have local singularities, such as sharp fronts. Traditional nonlinear iterative methods, such as Newton-like methods, are capable of reducing the global smooth nonlinearities at a nearly quadratic convergence rate but may become very slow once the local singularities appear somewhere in the computational domain. Even with global strategies such as line search or trust region the methods often stagnate at local minima of {parallel}F{parallel}, especially for problems with unbalanced nonlinearities, because the methods do not have built-in machinery to deal with the unbalanced nonlinearities. To find the same solution u* of F(u) = 0, we solve, instead, an equivalent nonlinearly preconditioned system G(F(u*)) = 0 whose nonlinearities are more balanced. In this project, we proposed and studied a nonlinear additive Schwarz based parallel nonlinear preconditioner and showed numerically that the new method converges well even for some difficult problems, such as high Reynolds number flows, when a traditional inexact Newton method fails.

Cited by 3Open access

Optimal Fourth-Order Iterative Methods for Solving Nonlinear Equations

I. A. Al-Subaihi · International Journal of Mathematics Trends and Technology · 2014

This paper presents a new optimal fourth-order iterative methods for solving nonlinear equations f(x)=0. The proposed iterative methods are obtained by composing the fourth-order iterative family method proposed by King 1973 with the ellipse method described by Gupta et al.(1998), which is always defined even if the first directive of the function at a point is zero. The convergence analysis of the proposed iterative methods was performed. Several numerical examples are also considered to illustrate the efficiency and the accuracy of the proposed iterative methods.

Cited by 2Open access

Derivative Free Conformable Iterative Methods for Solving Nonlinear Equations

Giro Candelario, Alicia Cordero, Juan R. Torregrosa et al. · Preprints.org · 2023

In the last years, a recent growing line of research has been developed with fruitful results by using fractional and conformable derivatives in the iterative procedures of classical methods for solving nonlinear equations. In that sense, the use of conformable derivatives has shown better behavior than fractional ones, not only in the theory, but also in the practice. In this work, we adapt the approximation of conformable derivatives in order to design the first conformable derivative-free iterative schemes to solve nonlinear equations: a Steffensen’s type method and a Secant type method; the latter with memory. Convergence analysis is made, preserving the order of classical cases, and the numerical performance is studied in order to confirm the results in the theory. It is shown that these methods can present some numerical advantages versus their classical partners, with wide sets of converging initial estimations.

Cited by 0Open access