EMAHAMAN METODE NUMERIK (STUDI KASUS METODE NEW-RHAPSON) MENGGUNAKAN PEMPROGRMAN MATLAB

2017 ◽  
Vol 1 (1) ◽  
pp. 95
Author(s):  
Siti Nurhabibah Hutagalung

Abstract - The study of the characteristics of non-liier functions can be carried out experimentally and theoretically. One part of theoretical analysis is computation. For computational purposes, numerical methods can be used to solve equations complicated, for example non-linear equations. There are a number of numerical methods that can be used to solve nonlinear equations, the Newton-Raphson method. Keywords - Numerical, Newton Raphson.

2021 ◽  
Vol 23 (07) ◽  
pp. 858-866
Author(s):  
Gauri Thakur ◽  
◽  
J.K. Saini ◽  

In numerical analysis, methods for finding roots play a pivotal role in the field of many real and practical applications. The efficiency of numerical methods depends upon the convergence rate (how fast the particular method converges). The objective of this study is to compare the Bisection method, Newton-Raphson method, and False Position Method with their limitations and also analyze them to know which of them is more preferred. Limitations of these methods have allowed presenting the latest research in the area of iterative processes for solving non-linear equations. This paper analyzes the field of iterative methods which are developed in recent years with their future scope.


Author(s):  
Umair Khalid Qureshi

This article is presented a modified quadrature iterated methods of Boole rule and Weddle rule for solving non-linear equations which arise in applied sciences and engineering. The proposed methods are converged quadratically and the idea of developed research comes from Boole rule and Weddle rule. Few examples are demonstrated to justify the proposed method as the assessment of the newton raphson method, steffensen method, trapezoidal method, and quadrature method. Numerical results and graphical representations of modified quadrature iterated methods are examined with C++ and EXCEL. The observation from numerical results that the proposed modified quadrature iterated methods are performance good and well executed as the comparison of existing methods for solving non-linear equations.


2019 ◽  
Vol 21 (1) ◽  
pp. 21-31
Author(s):  
Patrisius Batarius ◽  
Alfri Aristo SinLae

Determining the root of an equation means making the equation equal zero, (f (f) = 0). In engineering, there are often complex mathematical equations. With the numerical method approach, the equation can be searching for the value of the equation root. However, to find a double root approach with several numerical methods such as the bisection method, regulatory method, Newton-Raphson method, and Secant method, it is not efficient in determining multiple roots. This study aims to determine the roots of non-linear equations that have multiple roots using the modified Secant method. Besides knowing the effect of determining the initial value for the Secant method that is modifying in determining the non-linear root of persistence that has multiple roots. Comparisons were also make to other numerical methods in determining twin roots with the modified Secant method. A comparison is done to determine the initial value used. Simulations are performing on equations that have one single root and two or more double roots.


2020 ◽  
Vol 3 (2) ◽  
pp. 155-160
Author(s):  
Vera Mandailina ◽  
Syaharuddin Syaharuddin ◽  
Dewi Pramita ◽  
Malik Ibrahim ◽  
Habib Ratu Perwira Negara

Some of the numeric methods for solutions of non-linear equations are taken from a derivative of the Taylor series, one of which is the Newton-Raphson method. However, this is not the only method for solving cases of non-linear equations. The purpose of the study is to compare the accuracy of several derivative methods of the Taylor series of both single order and two-order derivatives, namely Newton-Raphson method, Halley method, Olver method, Euler method, Chebyshev method, and Newton Midpoint Halley method. This research includes qualitative comparison types, where the simulation results of each method are described based on the comparison results. These six methods are simulated with the Wilkinson equation which is a 20-degree polynomial. The accuracy parameters used are the number of iterations, the roots of the equation, the function value f (x), and the error. Results showed that the Newton Midpoint Halley method was the most accurate method. This result is derived from the test starting point value of 0.5 to the equation root x = 1, completed in 3 iterations with a maximum error of 0.0001. The computational design and simulation of this iterative method which is a derivative of the two-order Taylor series is rarely found in college studies as it still rests on the Newton-Raphson method, so the results of this study can be recommended in future learning.


Author(s):  
Vassilios Pachidis ◽  
Ioannis Templalexis ◽  
Pericles Pilidis

One of the most frequently encountered problems in engineering is dealing with non-linear equations. For example, the solution of the full Radial Equilibrium Equation (REE) in Streamline Curvature (SLC) through-flow methods is a typical case of a scientific analysis associated with a complex mathematical problem that can not be handled analytically. Various schemes are used routinely in scientific studies for the numerical solution of mathematical problems. In simple cases, these methods can be applied in their original form with success. The Newton-Raphson for example is one such scheme, commonly employed in simple engineering problems that require an iterative solution. Frequently however, the analysis of more complex phenomena may fall beyond the range of applicability of ‘textbook’ numerical methods, and may demand the design of more dedicated algorithms for the mathematical solution of a specific problem. These algorithms can be empirical in nature, developed from scratch, or the combination of previously established techniques. In terms of robustness and efficiency, all these different schemes would have their own merits and shortcomings. The success or failure of the numerical scheme applied depends also on the limitations imposed by the physical characteristics of the computational platform used, as well as by the nature of the problem itself. The effects of these constraints need to be assessed and taken into account, so that they can be anticipated and controlled. This manuscript discusses the development, validation and deployment of a convergence algorithm for the fast, accurate and robust numerical solution of the non-linear equations of motion for two-dimensional flow fields. The algorithm is based on a hybrid scheme, combining the Secant and Bisection iteration methods. Although it was specifically developed to address the computational challenges presented by SLC-type of analyses, it can also be used in other engineering problems. The algorithm was developed to provide a mid-of-the-range option between the very efficient but notoriously unstable Newton-Raphson scheme and other more robust, but less efficient schemes, usually employing some sort of Dynamic Convergence Control (DCC). It was also developed to eliminate the large user intervention, usually required by standard numerical methods. This new numerical scheme was integrated into a compressor SLC software and was tested rigorously, particularly at compressor operating regimes traditionally exhibiting convergence difficulties (i.e. part-speed performance). The analysis showed that the algorithm could successfully reach a converged solution, equally robustly but much more efficiently compared to a hybrid Newton-Raphson scheme employing DCC. The performance of these two schemes, in terms of speed of execution, is presented here. Typical error histories and comparisons of simulated results against experimental are also presented in this manuscript for a particular case-study.


Author(s):  
Sanaullah Jamali

In this article, an iterative, bracketing and derivative-free method have been proposed with the second-order of convergence for the solution of non-linear equations. The proposed method derives from the Stirling interpolation technique, Stirling interpolation technique is the process of using points with known values or sample points to estimate values at unknown points or polynomials. All types of problems (taken from literature) have been tested by the proposed method and compared with existing methods (regula falsi method, secant method and newton raphson method) and it’s noted that the proposed method is more rapidly converges as compared to all other existing methods. All problems were solved by using MATLAB Version: 8.3.0.532 (R2014a) on my personal computer with specification Intel(R) Core (TM) i3-4010U CPU @ 1.70GHz with RAM 4.00GB and Operating System: Microsoft Windows 10 Enterprise Version 10.0, 64-Bit Server, x64-based processor.


Author(s):  
Maulia Putri ◽  
Syaharuddin Syaharuddin

Non-linear equations are one of the studies in mathematics. Root search in complex non-linear equations can be solved by numerical methods. Many methods to solve the equation. Therefore, the purpose of this research is to conduct simulation of closed and open methods such as Newton Raphson method, Secant method, Regula Falsi, Fixet Point, and Bisection. This is done as a form of comparative research to see the accuracy, number of iterations, and errors of each method in resolving the non-linear equations. As for the case being resolved is the roots of the exponential equation, trigonometry, logarithmic and polynomial degrees of three. The results of this study resulted in different levels of convergence in resolving each case


2019 ◽  
Vol 8 (1) ◽  
pp. 336-342
Author(s):  
Siti Asilah Yah ◽  
Naimah Yaakob ◽  
Mohamed Elshaikh Elobaid ◽  
Ong Bi Lynn ◽  
R. Badlishah ◽  
...  

Nowadays, Vehicular Ad-Hoc Network (VANET) has got more attention from the researchers. The researchers have studied numerous topics of VANET, such as the routing protocols of VANET and the MAC protocols of VANET. The aim of their works is to improve the network performance of VANET, either in terms of energy consumption or packet delivery ratio (PDR) and delay. For this research paper, the main goal is to find the coefficient of a, b and c of three non-linear equations by using a Newton- Raphson method. Those three non-linear equations are derived from a different value of Medium Access Control (MAC) protocol's parameters. After that, those three coefficient is then will be used in optimization of the VANET in terms of energy, PDR, and delay.


Author(s):  
Siti Asilah Yah ◽  
Naimah Yaakob ◽  
Mohamed Elshaikh Elobaid ◽  
Ong Bi Lynn ◽  
R. Badlishah ◽  
...  

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