scholarly journals New Simpson type method for solving nonlinear equations

2021 ◽  
Vol 5 (1) ◽  
pp. 94-100
Author(s):  
U. K. Qureshi ◽  
◽  
A. A. Shaikhi ◽  
F. K. Shaikh ◽  
S. K. Hazarewal ◽  
...  
Keyword(s):  
Applied Sciences ◽  
Numerical Methods ◽  
Nonlinear Equation ◽  
Nonlinear Equations ◽  
Real World ◽  
Convergence Order ◽  
Type Method ◽  
Numerical Examples ◽  
The Real ◽  
Better Than

Finding root of a nonlinear equation is one of the most important problems in the real world, which arises in the applied sciences and engineering. The researchers developed many numerical methods for estimating roots of nonlinear equations. The this paper, we proposed a new Simpson type method with the help of Simpson 1/3rd rule. It has been proved that the convergence order of the proposed method is two. Some numerical examples are solved to validate the proposed method by using C++/MATLAB and EXCEL. The performance of proposed method is better than the existing ones.

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

scholarly journals On an Aitken-Steffensen-Newton type method

2018 ◽  
Vol 34 (1) ◽  
pp. 85-92
Author(s):  
ION PAVALOIU ◽  
Keyword(s):  
Local Convergence ◽  
Convergence Result ◽  
Convergence Order ◽  
Monotone Convergence ◽  
Type Method ◽  
Numerical Examples ◽  
Newton Iterations ◽  
Convergence Orders

We consider an Aitken-Steffensen type method in which the nodes are controlled by Newton and two-step Newton iterations. We prove a local convergence result showing the q-convergence order 7 of the iterations. Under certain supplementary conditions, we obtain monotone convergence of the iterations, providing an alternative to the usual ball attraction theorems. Numerical examples show that this method may, in some cases, have larger (possibly sided) convergence domains than other methods with similar convergence orders.

scholarly journals A family of two-point methods with memory for solving nonlinear equations

2011 ◽  
Vol 5 (2) ◽  
pp. 298-317 ◽  
Author(s):  
Miodrag Petkovic ◽  
Jovana Dzunic ◽  
Ljiljana Petkovic
Keyword(s):  
Nonlinear Equations ◽  
Free Parameter ◽  
Convergence Order ◽  
Optimal Order ◽  
Additional Function ◽  
Numerical Examples ◽  
Derivative Free ◽  
With Memory ◽  
Theoretical Results ◽  
High Computational Efficiency

An efficient family of two-point derivative free methods with memory for solving nonlinear equations is presented. It is proved that the convergence order of the proposed family is increased from 4 to at least 2 + ?6 ? 4.45, 5, 1/2 (5 + ?33) ? 5.37 and 6, depending on the accelerating technique. The increase of convergence order is attained using a suitable accelerating technique by varying a free parameter in each iteration. The improvement of convergence rate is achieved without any additional function evaluations meaning that the proposed methods with memory are very efficient. Moreover, the presented methods are more efficient than all existing methods known in literature in the class of two-point methods and three-point methods of optimal order eight. Numerical examples and the comparison with the existing two-point methods are included to confirm theoretical results and high computational efficiency. 2010 Mathematics Subject Classification. 65H05

scholarly journals Families of optimal multipoint methods for solving nonlinear equations: A survey

2010 ◽  
Vol 4 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Miodrag Petkovic ◽  
Ljiljana Petkovic
Keyword(s):  
Nonlinear Equations ◽  
Computational Efficiency ◽  
Rapid Development ◽  
Convergence Order ◽  
Important Class ◽  
Iterative Root ◽  
Numerical Examples ◽  
Multipoint Methods ◽  
The 1960S ◽  
Order Four

Multipoint iterative root-solvers belong to the class of the most powerful methods for solving nonlinear equations since they overcome theoretical limits of one-point methods concerning the convergence order and computational efficiency. Although the construction of these methods has occurred in the 1960s, their rapid development have started in the first decade of the 21-st century. The most important class of multipoint methods are optimal methods which attain the convergence order 2n using n + 1 function evaluations per iteration. In this paper we give a review of optimal multipoint methods of the order four (n = 2), eight (n = 3) and higher (n > 3), some of which being proposed by the authors. All of them possess as high as possible computational efficiency in the sense of the Kung-Traub hypothesis (1974). Numerical examples are included to demonstrate a very fast convergence of the presented optimal multipoint methods.

scholarly journals Further Acceleration of the Simpson Method for Solving Nonlinear Equations

2018 ◽  
Vol 14 (2) ◽  
pp. 7631-7639
Author(s):  
Rajinder Thukral
Keyword(s):  
Nonlinear Equation ◽  
Fourth Order ◽  
Efficiency Index ◽  
New Method ◽  
Order Method ◽  
Third Order ◽  
Type Method ◽  
New Formula ◽  
Order Four ◽  
Better Than

There are two aims of this paper, firstly, we present an improvement of the classical Simpson third-order method for finding zeros a nonlinear equation and secondly, we introduce a new formula for approximating second-order derivative. The new Simpson-type method is shown to converge of the order four.  Per iteration the new method requires same amount of evaluations of the function and therefore the new method has an efficiency index better than the classical Simpson method.  We examine the effectiveness of the new fourth-order Simpson-type method by approximating the simple root of a given nonlinear equation. Numerical comparisons is made with classical Simpson method to show the performance of the presented method.

Marketing Communication Menggunakan Augmented Reality pada Mobile Platform

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Julio Cristian Young
Keyword(s):  
Augmented Reality ◽  
Real World ◽  
Virtual World ◽  
Mobile Platform ◽  
Marketing Communication ◽  
Process Data ◽  
The Real ◽  
Graphical Data ◽  
Better Than

Augmented Reality is a technology that can project objects from the virtual world to the real world. Augmented Reality continues to be developed so it can be easy to implement into various devices. However, the device must have a camera, VGA card, and the ability to process data that is high enough to be able to process and projecting graphical data that captured by the camera and displayed to the screen. Marker-based Augmented Reality is still better than Markerless Augmented Reality due to several issues such as disturbances in the geomagnetic sensor that is used to map the Y axis and Z device that belongs to the user.

scholarly journals Real-World Performance of Longitudinal Barriers Struck by Large Trucks

2012 ◽  
Vol 2309 (1) ◽  
pp. 127-134 ◽  
Author(s):  
Douglas J. Gabauer
Keyword(s):  
Real World ◽  
Reporting System ◽  
Penetration Rate ◽  
Heavy Vehicles ◽  
The Real ◽  
Impact Performance ◽  
Passenger Vehicles ◽  
Road Users ◽  
The Impact ◽  
Better Than

Very little is known about the real-world performance of traffic barriers when subjected to impacts by large trucks. This study investigated real-world impacts of large trucks into traffic barriers to determine barrier crash involvement rates, the impact performance of barriers not specifically designed to redirect large trucks, and the real-world performance of barriers specifically designed for large trucks. Data sources included the Fatality Analysis Reporting System (2000 to 2009), the General Estimates System (2000 to 2009), and the Large Truck Crash Causation Study (155 in-depth crashes of large trucks into barriers). Impacts of large trucks into longitudinal barriers constituted 3% of all police-reported impacts into longitudinal barriers and roughly the same proportion of barrier fatalities. A logistic regression model predicting barrier penetration showed that the risk of a large truck penetrating a barrier increased by a factor of 6 for impacts with barriers designed primarily for passenger vehicles. Although barriers specifically designed for impacts by large trucks performed better than barriers not specifically designed for impacts by heavy vehicles, the penetration rate of the former was 17%. This penetration rate is of concern, because barriers used for higher test levels are designed to protect other road users, not the occupants of large trucks. Barriers not specifically designed for impacts by large trucks prevented penetration by a large truck approximately half the time. This finding suggests that adding costlier barriers that meet higher test levels may not always be warranted, especially on roadways with lower truck volumes.

scholarly journals A New Sixth-Order Steffensen-Type Iterative Method for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Tahereh Eftekhari
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Nonlinear Equations ◽  
Efficiency Index ◽  
Sixth Order ◽  
New Method ◽  
Derivative Free ◽  
Better Than

Based on iterative method proposed by Basto et al. (2006), we present a new derivative-free iterative method for solving nonlinear equations. The aim of this paper is to develop a new method to find the approximation of the root α of the nonlinear equation f(x)=0. This method has the efficiency index which equals 61/4=1.5651. The benefit of this method is that this method does not need to calculate any derivative. Several examples illustrate that the efficiency of the new method is better than that of previous methods.

A Modification of Newton-Type Method with Sixth-Order Convergence for Solving Nonlinear Equations

2012 ◽  
Vol 490-495 ◽  
pp. 1839-1843
Author(s):  
Rui Chen ◽  
Liang Fang
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Numerical Results ◽  
Sixth Order ◽  
Order Convergence ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present and analyze a modified Newton-type method with oder of convergence six for solving nonlinear equations. The method is free from second derivatives. It requires three evaluations of the functions and two evaluations of derivatives in each step. Therefore the efficiency index of the presented method is 1.431 which is better than that of classical Newton’s method 1.414. Some numerical results illustrate that the proposed method is more efficient and performs better than classical Newton's method

scholarly journals Convergence Analysis of a Three Step Newton-like Method for Nonlinear Equations in Banach Space under Weak Conditions

2016 ◽  
Vol 54 (2) ◽  
pp. 37-46
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Banach Space ◽  
Convergence Analysis ◽  
Nonlinear Equations ◽  
Local Convergence ◽  
Convergence Order ◽  
Order Method ◽  
Numerical Examples ◽  
Local Convergence Analysis

Abstract In the present paper, we study the local convergence analysis of a fifth convergence order method considered by Sharma and Guha in [15] to solve equations in Banach space. Using our idea of restricted convergence domains we extend the applicability of this method. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.

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