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Journal articles on the topic 'Newton-Raphson method'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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1

Torres-Hernandez, A., and F. Brambila-Paz. "Fractional Newton-Raphson Method." Applied Mathematics and Sciences An International Journal (MathSJ) 8, no. 1 (March 31, 2021): 1–13. http://dx.doi.org/10.5121/mathsj.2021.8101.

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The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n, with n ∈ N. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real initial condition is taken. In the present work, we explain an iterative method that is created using the fractional calculus, which we will call the Fractional Newton-Raphson (F N-R) Method, which has the ability to enter the space of complex numbers given a real initial condition, which allows us to find both the real and complex roots of a polynomial unlike the classical Newton-Raphson method.

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2

Verbeke, Johan, and Ronald Cools. "The Newton‐Raphson method." International Journal of Mathematical Education in Science and Technology 26, no. 2 (March 1995): 177–93. http://dx.doi.org/10.1080/0020739950260202.

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3

Mehtre, Vishal V. "Root Finding Methods: Newton Raphson Method." International Journal for Research in Applied Science and Engineering Technology 7, no. 11 (November 30, 2019): 411–14. http://dx.doi.org/10.22214/ijraset.2019.11065.

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4

Maxrizal, Maxrizal. "Modifikasi Garis Singgung Untuk Mempercepat Iterasi Pada Metode Newton Raphson." Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi 11, no. 2 (December 14, 2023): 351–60. http://dx.doi.org/10.37905/euler.v11i2.23094.

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The Newton-Raphson method is one of the methods to find solutions or roots of nonlinear equations. This method converges faster than other methods and is more effective in finding doubles. In this study, it will be shown that the Newton-Raphson modification uses modifications to the tangent equation. The results show that for every nth iteration, the speed difference of Newton Raphson modification is __. Furthermore, the convergence of Newton Raphson is __, and for Newton Raphson modification is __.

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5

RAMADHANI UTAMI, NANDA NINGTYAS, I. NYOMAN WIDANA, and NI MADE ASIH. "PERBANDINGAN SOLUSI SISTEM PERSAMAAN NONLINEAR MENGGUNAKAN METODE NEWTON-RAPHSON DAN METODE JACOBIAN." E-Jurnal Matematika 2, no. 2 (May 31, 2013): 11. http://dx.doi.org/10.24843/mtk.2013.v02.i02.p032.

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System of nonlinear equations is a collection of some nonlinear equations. The Newton-Raphson method and Jacobian method are methods used for solving systems of nonlinear equations. The Newton-Raphson methods uses first and second derivatives and indeed does perform better than the steepest descent method if the initial point is close to the minimizer. Jacobian method is a method of resolving equations through iteration process using simultaneous equations. If the Newton-Raphson methods and Jacobian methods are compared with the exact value, the Jacobian method is the closest to exact value but has more iterations. In this study the Newton-Raphson method gets the results faster than the Jacobian method (Newton-Raphson iteration method is 5 and 58 in the Jacobian iteration method). In this case, the Jacobian method gets results closer to the exact value.

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6

Mehtre, Vishal Vaman. "Review on Newton Raphson Method." International Journal for Research in Applied Science and Engineering Technology 7, no. 11 (November 30, 2019): 669–71. http://dx.doi.org/10.22214/ijraset.2019.11107.

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7

Ng, S. W., and Y. S. Lee. "Variable dimension Newton-Raphson method." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 47, no. 6 (June 2000): 809–17. http://dx.doi.org/10.1109/81.852933.

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8

He, Ji-Huan. "A modified Newton-Raphson method." Communications in Numerical Methods in Engineering 20, no. 10 (June 10, 2004): 801–5. http://dx.doi.org/10.1002/cnm.664.

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9

Qureshi, Umair Khalid, Sanaullah Jamali, Zubair Ahmed Kalhoro, and Guan Jinrui. "Deprived of Second Derivative Iterated Method for Solving Nonlinear Equations." Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences 58, no. 2 (December 24, 2021): 39–44. http://dx.doi.org/10.53560/ppasa(58-2)605.

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Non-linear equations are one of the most important and useful problems, which arises in a varied collection of practical applications in engineering and applied sciences. For this purpose, in this paper has been developed an iterative method with deprived of second derivative for the solution of non-linear problems. The developed deprived of second derivative iterative method is convergent quadratically, and which is derived from Newton Raphson Method and Taylor series. The numerical results of the developed method are compared with the Newton Raphson Method and Modified Newton Raphson Method. From graphical representation and numerical results, it has been observed that the deprived of second derivative iterative method is more appropriate and suitable as accuracy and iteration perception by the valuation of Newton Raphson Method and Modified Newton Raphson Method for estimating a non-linear problem.

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10

Syafii, Mohamad, Rahmi Ridhallah, and Rizki Amalia Nur. "Penerapan Metode Newton Raphson untuk Pencarian Akar pada Fungsi Kompleks." JOSTECH Journal of Science and Technology 3, no. 1 (March 31, 2023): 71–78. http://dx.doi.org/10.15548/jostech.v3i1.5685.

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This study aims to compare analytical methods and numerical methods in determining the roots of equations of a complex function. The numerical method used in this research is the Newton Raphson method. In this study two examples of complex functions were given, after which the roots of the equation were searched using the analytical method and the Newton Raphson method, then the results were compared. In this study, two examples are given, namely and . In example one, three different roots were obtained analytically, while numerical calculations using the Newton Raphson method obtained a value that converged to one of the roots that had been obtained analytically. In example two, four different roots were obtained analytically, while numerically using the Newton Raphson method similarly if done using the Newton Raphson method, a value that converged to one of the roots that had been obtained analytically was obtained.

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11

Herdiana, Indra, Idha Sihwaningrum, and Agus Sugandha. "THE NEWTON-RAPHSON METHOD OF REAL-VALUED FUNCTIONS IN DISCRETE METRIC SPACE." Jurnal Ilmiah Matematika dan Pendidikan Matematika 15, no. 2 (January 15, 2024): 113. http://dx.doi.org/10.20884/1.jmp.2023.15.2.8875.

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This paper studies the Newton-Raphson method to approximate a root of a real-valued function in one-dimensional real discrete metric space. The method involves a derivative and is considered to be convergent very fast. However, the derivative is derived from the limit definition with respect to the Euclidean distance, different from that of the discrete metric space. This research investigates the Newton-Raphson method with respect to derivatives defined in discrete metric spaces by deriving the derivative first. The results show that the constructed Newton-Raphson method can be an alternative root-finding method exemplified by some examples. Keywords: Newton-Raphson method, discrete metric space, metric space derivative

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12

Fang, Liang, and Lin Pang. "Improved Newton-Raphson Methods for Solving Nonlinear Equations." JOURNAL OF ADVANCES IN MATHEMATICS 13, no. 5 (December 25, 2017): 7403–7. http://dx.doi.org/10.24297/jam.v13i5.6533.

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In this paper, we mainly study the numerical algorithms for simple root of nonlinear equations based on Newton-Raphson method. Two modified Newton-Raphson methods for solving nonlinear equations are suggested. Both of the methods are free from second derivatives. Numerical examples are made to show the performance of the presented methods, and to compare with other ones. The numerical results illustrate that the proposed methods are more efficient and performs better than Newton-Raphson method.

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13

Tohtayong, Majdee, Sheroz Khan, Mashkuri Yaacob, Siti Hajar Yusoff, Nur Shahida Midi, Musse Mohamud Ahmed, Fawwaz Wafa, Ezzidin Aboadla, and Khairil Azhar Aznan. "The Combination of Newton-Raphson Method and Curve-Fitting Method for PWM-based Inverter." International Journal of Power Electronics and Drive Systems (IJPEDS) 8, no. 4 (December 1, 2017): 1919. http://dx.doi.org/10.11591/ijpeds.v8.i4.pp1919-1931.

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<span>This paper presents the combination of two different methods to perform the waveform analysis for PWM-operated inverter. The two techniques are Newton-Raphson method and Curve-Fitting as a PWM concept to operate PWM-based inverter, the proper solutions of switching angles can valuate the initial values by using the Newton-Raphson method with the wide-step calculation of modulation indices. The solutions are then compared using a curve in order to study the behavior. Then, the Curve-Fitting method is used to estimate the missing solutions between any points of wide-step calculation. This combination method can estimate the probable solutions that cannot be solved by Newton-Raphson method in a wide-ranging of the modulation index and reduce the calculation time. PWM-based inverter, which is obtained the switching angles by Newton-Raphson method and the combination of two different methods, is verified by the simulation results showing faster performance with improved Total Harmonic Distortion (THD) than both methods alone when compared the same values of switching angles.</span>

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14

Bayrak, Mine Aylin, Ali Demir, and Ebru Ozbilge. "On Fractional Newton-Type Method for Nonlinear Problems." Journal of Mathematics 2022 (November 21, 2022): 1–10. http://dx.doi.org/10.1155/2022/7070253.

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The current manuscript is concerned with the development of the Newton–Raphson method, playing a significant role in mathematics and various other disciplines such as optimization, by using fractional derivatives and fractional Taylor series expansion. The development and modification of the Newton–Raphson method allow us to establish two new methods, which are called first- and second-order fractional Newton–Raphson (FNR) methods. We provide convergence analysis of first- and second-order fractional methods and give a general condition for the convergence of higher-order FNR. Finally, some illustrative examples are considered to confirm the accuracy and effectiveness of both methods.

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15

Tien Tay, Lea, William Ong Chew Fen, and Lilik Jamilatul Awalin. "Improved newton-raphson with schur complement methods for load flow analysis." Indonesian Journal of Electrical Engineering and Computer Science 16, no. 2 (November 1, 2019): 699. http://dx.doi.org/10.11591/ijeecs.v16.i2.pp699-605.

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<p>The determination of power and voltage in the power load flow for the purpose of design and operation of the power system is very crucial in the assessment of actual or predicted generation and load conditions. The load flow studies are of the utmost importance and the analysis has been carried out by computer programming to obtain accurate results within a very short period through a simple and convenient way. In this paper, Newton-Raphson method which is the most common, widely-used and reliable algorithm of load flow analysis is further revised and modified to improve the speed and the simplicity of the algorithm. There are 4 Newton-Raphson algorithms carried out, namely Newton-Raphson, Newton-Raphson constant Jacobian, Newton-Raphson Schur Complement and Newton-Raphson Schur Complement constant Jacobian. All the methods are implemented on IEEE 14-, 30-, 57- and 118-bus system for comparative analysis using MATLAB programming. The simulation results are then compared for assessment using measurement parameter of computation time and convergence rate. Newton-Raphson Schur Complement constant Jacobian requires the shortest computational time.</p>

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16

Wang, Zhao Qing, Jian Jiang, Bing Tao Tang, and Wei Zheng. "Barycentric Interpolation Newton-Raphson Iterative Method for Solving Nonlinear Beam Equations." Applied Mechanics and Materials 684 (October 2014): 41–48. http://dx.doi.org/10.4028/www.scientific.net/amm.684.41.

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A barycentric interpolation Newton-Raphson iterative method for solving nonlinear beam bending problems is presented in this article. The nonlinear governing differential equation of beam bending problem is discretized by barycentric interpolation collocation method to form a system of nonlinear algebraic equations. Newton-Raphson iterative method is applied to solve the system of nonlinear algebraic equations. The Jacobian derivative matrix in Newton-Raphson iterative method is formulated by the Hadamard product of vectors. Some numerical examples are given to demonstrate the validity and accuracy of proposed method.

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17

Pho, Kim-Hung. "Improvements of the Newton–Raphson method." Journal of Computational and Applied Mathematics 408 (July 2022): 114106. http://dx.doi.org/10.1016/j.cam.2022.114106.

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18

Bora, Toralima, and G. C. Hazarika. "Newton Raphson Method using Fuzzy Concept." International Journal of Mathematics Trends and Technology 42, no. 1 (February 25, 2017): 36–38. http://dx.doi.org/10.14445/22315373/ijmtt-v42p505.

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19

Bora, Toralima, and G. C. "Comparative Study between Fuzzified Newton Raphson Method and Original Newton Raphson Method and its Computer Application." International Journal of Computer Applications 164, no. 10 (April 17, 2017): 12–14. http://dx.doi.org/10.5120/ijca2017913703.

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20

Nabiyah, Ismi Ratin, Opim Salim, and Tulus Tulus. "The development of Newton’s method by enhancing the starting point." International Journal of Trends in Mathematics Education Research 6, no. 1 (March 30, 2023): 12–18. http://dx.doi.org/10.33122/ijtmer.v6i1.205.

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In general, nonlinear problems cannot be solved analytically. A special theory or method is needed to simplify calculations. Many problems that are too complex, an exact solution is needed to support numerical solution. There are many numerical methods that can be used to solve nonlinear problems, including the Bisection, Secant and Newton methods, also known as the Newton-Raphson method. However, these methods cannot be used for large-scale of nonlinear programming problems; for example the Newton-Raphson method which does not always converge if it takes the wrong initial value. The Newton-Raphson method is widely used to find approximations to the roots of real functions. However, the Newton-Raphson method does not always converge if it takes the wrong initial value. Therefore, it is necessary to develop the Newton-Raphson method without using other methods in order to have a higher convergence. This research is a literature study compiled based on literature references with the initial step of understanding problems that appear from the use of Newton's method, it is base on the problem of divergence or oscillation. Newtonian method was developed without modification of other methods, but took two starting points. Then prove the super-quadratic convergence of the proposed method by extending the Taylor expansion and giving or assuming the error rate. After that, the stability test of the proposed model is carried out and provides an example of the application by solving the root search using Newton's method and the proposed method can be seen as a comparison.

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21

Torres-Hernandez, A., F. Brambila-Paz, U. Iturrarán-Viveros, and R. Caballero-Cruz. "Fractional Newton–Raphson Method Accelerated with Aitken’s Method." Axioms 10, no. 2 (March 31, 2021): 47. http://dx.doi.org/10.3390/axioms10020047.

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In the following paper, we present a way to accelerate the speed of convergence of the fractional Newton–Raphson (F N–R) method, which seems to have an order of convergence at least linearly for the case in which the order α of the derivative is different from one. A simplified way of constructing the Riemann–Liouville (R–L) fractional operators, fractional integral and fractional derivative is presented along with examples of its application on different functions. Furthermore, an introduction to Aitken’s method is made and it is explained why it has the ability to accelerate the convergence of the iterative methods, in order to finally present the results that were obtained when implementing Aitken’s method in the F N–R method, where it is shown that F N–R with Aitken’s method converges faster than the simple F N–R.

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22

A. Triantafyllou, Serafeim. "Conceptualización del método iterativo de Newton-Raphson para sistemas con dos ecuaciones." Salud, Ciencia y Tecnología - Serie de Conferencias 2 (January 31, 2024): 525. http://dx.doi.org/10.56294/sctconf2023525.

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In numerical analysis, Newton-Raphson method is a root-finding algorithm which generates iterative approximations to the zeroes (or roots) of a real-valued function. This paper describes in a detailed way the mathematical background around the iterative method of Newton-Raphson for systems with two equations. Next, an algorithmic implementation of the iterative method of Newton-Raphson for systems with two equations is developed in Pascal Programming Language, to represent the steps of this method with a procedural programming language with special emphasis on the use of computing in the scientific area of mathematics.

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23

Song, Shu Ni, Jing Yi Liu, and Jin Qian. "Application of an Improved Trust-Region Method to Rigid-Plastic Finite Element Analysis in Strip Rolling." Materials Science Forum 704-705 (December 2011): 216–22. http://dx.doi.org/10.4028/www.scientific.net/msf.704-705.216.

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Rigid-plastic finite element analysis (RPFEA) is an efficient and practical method to calculate rolling parameters in the strip rolling process. To solve the system of simulations equations involved in the RPFEA, a numerous of numerical methods, including the standard Newton-Raphson method, the modified Newton-Raphson method, and etc., have been proposed by different researchers. However, the computational time of the existed numerical methods can not meet the requirement of the online application. By tracking the computational time consumption for the main components in the standard Newton-Raphson method used in finite element analysis, it was found that linear search of damping factor occupies the most of the computational time. Thus, more efforts should be put on the linear search of damping factor to speed up the solving procedure, so that the online application of RPFEA is possible. In this paper, an improved trust-region method is developed to speed up the solving procedure, in which the Hessian matrix is forced to positive definite so as to improve the condition number of matrix. The numerical experiments are carried out to compare the proposed method with the standard Newton-Raphson method based on the practical data collected from a steel company in China. The numerical results demonstrate that the computational time of the proposed method outperforms that of the standard Newton-Raphson method and can meet the requirement of online application. Meanwhile the computational values of rolling force obtained by the proposed method are in good agreement with experimental values, which verifies the validity and stability of the proposed method.

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24

Hawong, Jai Sug, and Konstantin Teche. "A Study on the New Static Photoelastic Experimental Hybrid Method." Key Engineering Materials 297-300 (November 2005): 2187–94. http://dx.doi.org/10.4028/www.scientific.net/kem.297-300.2187.

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In photoelastic experimental method, until now, we have used the Newton-Raphson numerical method in analysis of photoelastic experimental data such as the non-linear least square method for the photoelastic expreriment. We used the Hook-Jeeves’ numerical method in stead of Newton-Raphson numerical method for the non-linear least square method for photoelastic experimental method. The new photoelastic experimental hybrid method, that is, the photoelastic experimental hybrid method with Hook-Jeeves’ numerical method has been developed in this research. Applying the new photoelastic experimental hybrid method to stress concentration problems and plane fracture problems, it’s validity was assured. The new photoelastic experimental hybrid method is more precise and stabler than the photoelastic experimental hybrid method with Newton- Raphson numerical method (the old photoelastic experimental hybrid method)

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25

Pang, Weichao, Fujun Qi, Jun Wang, Fuqiang Zhao, Qijun Song, and Xingyu Pan. "A Power Flow Calculation Method Considering High-order Load Models." Journal of Physics: Conference Series 2527, no. 1 (June 1, 2023): 012020. http://dx.doi.org/10.1088/1742-6596/2527/1/012020.

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Abstract Given the popularity of new energy and the connection between large power electronic equipment and power system, the operation of power system becomes more complex and requires higher accuracy of power flow calculation. Therefore, a power flow calculation method considering high-order load model is proposed. On the basis of the Newton-Raphson method, when considering the load voltage characteristics, it is necessary to change the variables in the Newton-Raphson method power flow. Therefore, the established polynomial load model is introduced into the Newton-Raphson method, and the effect becomes more obvious with the increase of the order. Finally, constant power, constant current, constant impedance load and fifth order load models are tested in IEEE14-bus system respectively to verify the good accuracy and robustness of the proposed method.

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26

Chauhan, Anushka. "A Study of Modified Newton-Raphson Method." Journal of University of Shanghai for Science and Technology 23, no. 08 (August 4, 2021): 129–34. http://dx.doi.org/10.51201/jusst/21/08359.

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A basic alteration of the standard Newton technique is investigated and described for the approximation of the roots of a univariate function. For a similar number of functions and evaluation of the derivative, an altered strategy combines quicker, with the convergence of the modified NR’s method being 2.4 as compared with the regular NR method which is 2. Some of the example shows the faster convergence accomplished with the modified NR method. This modification of Newton’s technique is generally basic and strong. It is bound to converge to the solution rather than the higher order or Newton-Raphson method itself. In this paper, the modification of NR strategy introduced which offers expanded rate of convergence over NR standard method.

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27

Ypma, Tjalling J. "Historical Development of the Newton–Raphson Method." SIAM Review 37, no. 4 (December 1995): 531–51. http://dx.doi.org/10.1137/1037125.

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28

Kulworawanichpong, Thanatchai. "Simplified Newton–Raphson power-flow solution method." International Journal of Electrical Power & Energy Systems 32, no. 6 (July 2010): 551–58. http://dx.doi.org/10.1016/j.ijepes.2009.11.011.

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29

Lee, In-Won, and Gil-Ho Jung. "A generalized Newton-Raphson method using curvature." Communications in Numerical Methods in Engineering 11, no. 9 (September 1995): 757–63. http://dx.doi.org/10.1002/cnm.1640110906.

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30

Souza, Luiz Antonio Farani de, Emerson Vitor Castelani, and Wesley Vagner Inês Shirabayashi. "Adaptation of the Newton-Raphson and Potra-Pták methods for the solution of nonlinear systems." Semina: Ciências Exatas e Tecnológicas 42, no. 1 (June 2, 2021): 63. http://dx.doi.org/10.5433/1679-0375.2021v42n1p63.

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In this paper we adapt the Newton-Raphson and Potra-Pták algorithms by combining them with the modified Newton-Raphson method by inserting a condition. Problems of systems of sparse nonlinear equations are solved the algorithms implemented in Matlab® environment. In addition, the methods are adapted and applied to space trusses problems with geometric nonlinear behavior. Structures are discretized by the Finite Element Positional Method, and nonlinear responses are obtained in an incremental and iterative process using the Linear Arc-Length path-following technique. For the studied problems, the proposed algorithms had good computational performance reaching the solution with shorter processing time and fewer iterations until convergence to a given tolerance, when compared to the standard algorithms of the Newton-Raphson and Potra-Pták methods.

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Triana Laverde, Juan Gabriel. "On the Newton-Raphson method and its modifications." Ciencia en Desarrollo 14, no. 2 (July 19, 2023): 75–80. http://dx.doi.org/10.19053/01217488.v14.n2.2023.15157.

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The Newton-Raphson method, also known as Newton's method, is a method for finding successively better approximations to the roots of a real-valued function, starting with an initial guess, being useful even for generating fractals when we consider complex functions. It is a fast method, but convergence is not guaranteed, which is the reason why several modifications of that method have been proposed. Here we present some modifications of the Newton-Raphson method, and we study the convergence of those methods through cases.

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32

Hiwarkar, Dr Chandrashekhar S., Abhay M. Halmare, Anurag A. Belsare, Nitin B. Mohriya, and Roshan Milmile. "Load Flow Analysis on IEEE 14 Bus System." International Journal for Research in Applied Science and Engineering Technology 10, no. 4 (April 30, 2022): 1572–74. http://dx.doi.org/10.22214/ijraset.2022.41590.

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Abstract: This article presents a load flow analysis of an IEEE14 BUS system using the Newton-Raphson method, which simplifies the analysis of load balancing problems. The software used for the programming platform is MATLAB. This paper gives an overview of the electrical performance and power flows (real and reactive) under a steady state. There are various methods for load flow computations. The gauss-seidel method is more popular in smaller systems because of less computational time. In the case of larger systems computation time increases in this condition, the Newton-Raphson method is preferred. This project aims to develop a MATLAB program to calculate voltages and active and reactive power at each bus for IEEE 14 bus systems. The MATLAB program is executed with the input data and results are compared. Keywords: load flow studies, Newton-Raphson method, IEEE 14 bus system.

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Juhari, Juhari. "On the Modification of Newton-Secant Method in Solving Nonlinear Equations for Multiple Zeros of Trigonometric Function." CAUCHY 7, no. 1 (November 12, 2021): 84–96. http://dx.doi.org/10.18860/ca.v7i1.12934.

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This study discusses the analysis of the modification of Newton-Secant method and solving nonlinear equations having a multiplicity of by using a modified Newton-Secant method. A nonlinear equation that has a multiplicity is an equation that has more than one root. The first step is to analyze the modification of the Newton-Secant method, namely to construct a mathematical model of the Newton-Secant method using the concept of the Newton method and the concept of the Secant method. The second step is to construct a modified mathematical model of the Newton-Secant method by adding the parameter . After obtaining the modified formula for the Newton-Secant method, then applying the method to solve a nonlinear equations that have a multiplicity . In this case, it is applied to the nonlinear equation which has a multiplicity of . The solution is done by selecting two different initial values, namely and . Furthermore, to determine the effectivity of this method, the researcher compared the result with the Newton-Raphson method, the Secant method, and the Newton-Secant method that has not been modified. The obtained results from the analysis of modification of Newton-Secant method is an iteration formula of the modified Newton-Secant method. And for the result of using a modified Newton-Secant method with two different initial values, the root of is obtained approximately, namely with less than iterations. whereas when using the Newton-Raphson method, the Secant method, and the Newton-Secant method, the root is also approximated, namely with more than iterations. Based on the problem to find the root of the nonlinear equation it can be concluded that the modified Newton-Secant method is more effective than the Newton-Raphson method, the Secant method, and the Newton-Secant method that has not been modified

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Taufik, Marhan, and Reni Dwi Susanti. "Solving numerical method problems with mathematical software: Identifying computational thinking." Pedagogical Research 9, no. 3 (July 1, 2024): em0209. http://dx.doi.org/10.29333/pr/14583.

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This research examines the application of students’ computational thinking (CT) in solving numerical method problems through computer software. Data collection involved observing their learning process and conducting tests to evaluate their CT skills within the context of the root approach material using Newton-Raphson method. The results indicate that the use of Microsoft Excel facilitates problem-solving for students and educators when employing Newton-Raphson method. Furthermore, it helps identify aspects or indicators of CT in students’ problem-solving processes. The research findings demonstrate that students with strong mathematical abilities should document their conclusions in the algorithmic aspect. Students with moderate mathematical abilities exhibit all indicators in every aspect of CT when solving problems using Newton-Raphson method. On the other hand, students with weak mathematical skills fail to articulate questions, formulas, or conclusions in the algorithm design aspect, but they do show all indicators in the pattern recognition and abstraction aspects.

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Mandailina, Vera, Syaharuddin Syaharuddin, Dewi Pramita, Malik Ibrahim, and Habib Ratu Perwira Negara. "Wilkinson Polynomials: Accuracy Analysis Based on Numerical Methods of the Taylor Series Derivative." Desimal: Jurnal Matematika 3, no. 2 (May 28, 2020): 155–60. http://dx.doi.org/10.24042/djm.v3i2.6134.

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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.

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Hutagalung, Siti Nurhabibah. "EMAHAMAN METODE NUMERIK (STUDI KASUS METODE NEW-RHAPSON) MENGGUNAKAN PEMPROGRMAN MATLAB." JURNAL TEKNOLOGI INFORMASI 1, no. 1 (June 1, 2017): 95. http://dx.doi.org/10.36294/jurti.v1i1.109.

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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.

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Al Shaltouni, Aya Al Shaltouni, and Abdulla Ismail. "Smart Load Flow Analysis using Conventional method and modern method." International Journal of Automation and Digital Transformation 2, no. 1 (December 23, 2023): 43–66. http://dx.doi.org/10.54878/kxtqe195.

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The optimal power flow for networked microgrids with different renewable energy sources (PV panels and wind turbines), storage systems, generators, and load is investigated in this study. A conventional method and an Artificial Intelligence method are applied to solve the OPF problem. The performance of MGs system with renewable energy integration was investigated in this study, with a focus on power flow studies. The power flow is calculated using the well-known Newton-Raphson method and the Neural Network method. The power flow calculation is used to assess grid performance parameters like voltage bus magnitude, angle, and real and reactive power flow in system transmission lines. under given load conditions. The standard test system used was a benchmark test system for Networked MGs with four MGs and 40 buses. The data for the entire system has been chosen as per the IEEE Standard 1547-2018. The results showed minimumlosses and higher efficiency when performing OPF using NN than the Newton-Raphson method. The efficiency of the power system for the networked MG is 99.3% using Neural Network and 97% using the Newton- Raphson method. The Neural Network method, which mimics how the human brain works based on AI technologies, gave the best results and better efficiency in both cases (Battery as Load/Battery as Source) than the conventional method.

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Shayya, W. H., R. H. Mohtar, and M. S. Baasiri. "A Computer Model for the Hydraulic Analysis of Open Channel Cross Sections." Journal of Agricultural and Marine Sciences [JAMS] 1 (January 1, 1996): 57. http://dx.doi.org/10.24200/jams.vol1iss0pp57-64.

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Irrigation and hydraulic engineers are often faced with the difficulty of tedious trial solutions of the Manning equation to determine the various geometric elements of open channels. This paper addresses the development of a computer model for the design of the most commonly used channel-sections. The developed model is intended as an educational tool. It may be applied to the hydraulic design of trapezoidal , rectangular, triangular, parabolic, round-concered rectangular, and circular cross sections. Two procedures were utilized for the solution of the encountered implicit equations; the Newton-Raphson and the Regula-Falsi methods. In order to initiate the solution process , these methods require one and two initial guesses, respectively. Tge result revealed that the Regula-Flasi method required more iterations to coverage to the solution compared to the Newton-Raphson method, irrespective of the nearness of the initial guess to the actual solution. The average number of iterations for the Regula-Falsi method was approximately three times that of the Newton-Raphson method.

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Huang, Yuan Mao, and C. D. Horng. "Analysis of Torsional Vibration Systems by the Extended Transfer Matrix Method." Journal of Vibration and Acoustics 121, no. 2 (April 1, 1999): 250–55. http://dx.doi.org/10.1115/1.2893972.

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This study applies the extended transfer matrix method and Newton-Raphson technique with complex numbers for torsional vibration analysis of damped systems. The relationships of the vibratory amplitude, the vibratory torque, the derivatives of the vibratory angular displacement and the vibratory torque between components at the left end and the right end of the torsional vibration system are derived. The derivatives of the vibratory angular displacement and the vibratory torque are used directly in the Newton-Raphson technique to determine the eigensolutions of systems that are compared and show good agreement with the available data.

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Mujeeb, Mujeebullah, Lutfullah Safi, and Ainullah Mirzazada. "Comparison of Newton Raphson – Linear Theory and Hardy Cross Methods Calculations for a Looped Water Supply Network." Journal of Natural Science Review 2, no. 2 (June 29, 2024): 75–90. http://dx.doi.org/10.62810/jnsr.v2i2.40.

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This study conducts a comparative analysis between the Newton-Raphson and Hardy Cross methods for solving a looped main linear water network consisting of 4 pipes. The research findings demonstrate a high degree of unity between the outcomes obtained from these two methods, thereby validating their accuracy and reliability in solving water network equations. While the Newton-Raphson method shows faster convergence than the Hardy-Cross Method, both approaches effectively plan and analyze water networks. The analytical methodology employed in this study provides valuable insights into the applicability and efficiency of these methods in optimizing gravity main water networks. By combining the strengths of the Newton-Raphson and Hardy Cross methods, engineers and planners can make informed decisions to enhance the performance and sustainability of water distribution systems. The findings contribute to advancements in water infrastructure planning and design, aiming to ensure efficient and reliable water supply to meet the evolving needs of urban and rural communities.

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Kocabaş, Derya. "Maximum MMF reduction using the Newton Raphson method." International Conference on Electrical Engineering 6, no. 6 (May 1, 2008): 1–12. http://dx.doi.org/10.21608/iceeng.2008.34295.

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Seng, Chieng Kai, Tay Lea Tien, Janardan Nanda, and Syafrudin Masri. "Load Flow Analysis Using Improved Newton-Raphson Method." Applied Mechanics and Materials 793 (September 2015): 494–99. http://dx.doi.org/10.4028/www.scientific.net/amm.793.494.

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This paper describes a simple, reliable and swift load-flow solution method with a wide range of practical application. It is attractive for accurate or approximate off-and on-line calculations for routine and contingency purposes. It is applicable for networks of any size and can be executed effectively on computers. The method is a development on conventional load flow principle and its precise algorithm form has been determined to bring improvement to the conventional techniques. This paper presents a comparative study of the new constant Jacobian matrix load flow method built based on several conventional NR load flow methods. Assumptions are made so as to make the matrix constant, thus eliminating the need of calculating the matrix in every iteration. The proposed method exhibits better computation speed.

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SCHNEEBELI, HANS RUDOLF, and THOMAS P. WIHLER. "THE NEWTON–RAPHSON METHOD AND ADAPTIVE ODE SOLVERS." Fractals 19, no. 01 (March 2011): 87–99. http://dx.doi.org/10.1142/s0218348x11005191.

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The Newton–Raphson method for solving nonlinear equations f(x) = 0 in ℝn is discussed within the context of ordinary differential equations. This framework makes it possible to reformulate the scheme by means of an adaptive step size control procedure that aims at reducing the chaotic behavior of the original method without losing the quadratic convergence close to the roots. The performance of the modified scheme is illustrated with a few low-dimensional examples.

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Spiliotis, M., and G. Tsakiris. "Water Distribution System Analysis: Newton-Raphson Method Revisited." Journal of Hydraulic Engineering 137, no. 8 (August 2011): 852–55. http://dx.doi.org/10.1061/(asce)hy.1943-7900.0000364.

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Yeo, Gwangoo, Seong-Jin Park, and Young-Hee Kim. "NEWTON-RAPHSON METHOD FOR COMPUTING p-ADIC ROOTS." Journal of the Chungcheong Mathematical Society 28, no. 4 (November 15, 2015): 575–82. http://dx.doi.org/10.14403/jcms.2015.28.4.575.

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Simons, Stuart. "90.21 A modification of the Newton-Raphson method." Mathematical Gazette 90, no. 517 (March 2006): 128–30. http://dx.doi.org/10.1017/s0025557200179240.

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Jamieson, M. J. "Newton–Raphson/log-derivative method for finding eigenenergies." Computer Physics Communications 125, no. 1-3 (March 2000): 193–95. http://dx.doi.org/10.1016/s0010-4655(99)00486-5.

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Hernández Paricio, Luis Javier. "Bivariate Newton-Raphson method and toroidal attraction basins." Numerical Algorithms 71, no. 2 (May 5, 2015): 349–81. http://dx.doi.org/10.1007/s11075-015-9996-3.

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Hauser, Raphael, and Jelena Nedic. "The Continuous Newton--Raphson Method Can Look Ahead." SIAM Journal on Optimization 15, no. 3 (January 2005): 915–25. http://dx.doi.org/10.1137/s1052623403432633.

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Chu, Time P., and W. H. Tang. "Newton-Raphson Method to Find the Optimal Ordering." OPSEARCH 36, no. 4 (December 1999): 343–59. http://dx.doi.org/10.1007/bf03398588.

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