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A new method of root finding is formulated that uses a numerical iterative process involving three points. A given function y = f(x) whose roots are desired is fitted and approximated by a polynomial function of the form P(x)= a(x-b)^N that…

Numerical Analysis · Mathematics 2013-02-11 Ababu Teklemariam Tiruneh , William N. Ndlela , Stanley J. Nkambule

In this paper we consider a boundary value problem for fully fourth order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation…

Numerical Analysis · Mathematics 2022-08-12 Dang Quang A , Nguyen Thanh Huong , Dang Quang Long

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…

Numerical Analysis · Mathematics 2016-02-24 Gunar Matthies , Mehdi Salimi , Somayeh Sharifi , Juan Luis Varona

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…

Numerical Analysis · Mathematics 2017-01-03 Bijaya Mishra , Ambit Kumar Pany , Salila Dutta

We proposed in this paper a new method, which we named the W4 method, to solve nonlinear equation systems. It may be regarded as an extension of the Newton-Raphson~(NR) method to be used when the method fails. Indeed our method can be…

Numerical Analysis · Mathematics 2022-04-22 Hirotada Okawa , Kotaro Fujisawa , Yu Yamamoto , Nobutoshi Yasutake , Misa Ogata , Shoichi Yamada

The present author recently proposed and proved a relationship theorem between nonlinear polynomial equations and the corresponding Jacobian matrix. By using this theorem, this paper derives a Newton iterative formula without requiring the…

Computational Engineering, Finance, and Science · Computer Science 2024-09-21 W. Chen

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…

Computational Physics · Physics 2010-12-30 Avas V. Khugaev , Renat A. Sultanov , D. Guster

We prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is…

Analysis of PDEs · Mathematics 2007-05-23 Andrea Malchiodi

We prove the sufficient conditions for convergence of a certain iterative process of order 2 for solving nonlinear functional equations, which does not require inverting the derivative. We translate and detail our results for a system of…

Numerical Analysis · Mathematics 2021-05-13 Tamara Kogan , Luba Sapir , Amir Sapir , Eytan Sapir

We present here the solution of the problem on linearization of fourth-order equations by means of point transformations. We show that all fourth-order equations that are linearizable by point transformations are contained in the class of…

Classical Analysis and ODEs · Mathematics 2007-10-26 Nail H. Ibragimov , Sergey V. Meleshko , Supaporn Suksern

In this paper, we present a three-point without memory iterative method based on Kung and Traub's method for solving non-linear equations in one variable. The proposed method has eighth-order convergence and costs only four function…

Numerical Analysis · Mathematics 2015-08-10 Gunar Matthies , Mehdi Salimi , Somayeh Sharifi , Juan Luis Varona

New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…

Numerical Analysis · Mathematics 2012-03-13 Joseph F. Grcar

We investigate the problem of entire solutions for a class of fourth order, dilation invariant, semilinear elliptic equations with power-type weights and with subcritical or critical growth in the nonlinear term. These equations define non…

Analysis of PDEs · Mathematics 2014-06-23 Paolo Caldiroli , Gabriele Cora

This manuscript presents a novel and reliable third-order iterative procedure for computing the zeros of solutions to second-order ordinary differential equations. By approximating the solution of the related Riccati differential equation…

Numerical Analysis · Mathematics 2026-01-08 Dhivya Prabhu K , Sanjeev Singh , Antony Vijesh

To extract the approximate solutions in the case of nonlinear fractional order differential equations with the homogeneous and nonhomogeneous boundary conditions, the weighted residual method is embedded here. We exploit three methods such…

Numerical Analysis · Mathematics 2024-04-05 Umme Ruman , Md. Shafiqul Islam

This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton-Raphson scheme. The original nonlinear system is first unfolded into three simpler…

Numerical Analysis · Mathematics 2014-07-24 Antonio Gómez-Expósito

In most introductory numerical analysis textbooks, the treatment of a single nonlinear equation often consists of a collection of all-purpose methods that frequently do not work or are inefficient. These textbooks neglect to teach the…

Numerical Analysis · Mathematics 2022-04-06 Aaron Melman

In this paper we consider the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed inverse problems. Under merely Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an…

Numerical Analysis · Mathematics 2009-11-13 Qinian Jin

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.

Numerical Analysis · Mathematics 2009-12-01 Cédric Boulbe , Tahar Zamène Boulmezaoud , T. Amari

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…

Numerical Analysis · Mathematics 2020-08-28 Sana Keita , Abdelaziz Beljadid , Yves Bourgault