scholarly journals Hybrid algorithm to Newton Raphson method and bisection method

2021 ◽  
Keyword(s):  
Hybrid Algorithm ◽  
Bisection Method ◽  
Newton Raphson ◽  
Raphson Method

An improved hybrid algorithm to bisection method and Newton-Raphson method

2017 ◽  
Vol 11 ◽  
pp. 2789-2797 ◽  
Author(s):  
Jeongwon Kim ◽  
Taehoon Noh ◽  
Wonjun Oh ◽  
Seung Park ◽  
Nahmwoo Hahm
Keyword(s):  
Hybrid Algorithm ◽  
Bisection Method ◽  
Newton Raphson ◽  
Raphson Method

Comparative Study of Iterative Methods for Solving Non-Linear Equations

2021 ◽  
Vol 23 (07) ◽  
pp. 858-866
Author(s):  
Gauri Thakur ◽  
◽  
J.K. Saini ◽  
Keyword(s):  
Numerical Analysis ◽  
Iterative Methods ◽  
Linear Equations ◽  
Bisection Method ◽  
Practical Applications ◽  
Non Linear ◽  
False Position ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

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.

scholarly journals Numerical Solution of Nonlinear Equations in Maple

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Qani Yalda
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Secant Method ◽  
Bisection Method ◽  
Real Roots ◽  
Newton Raphson ◽  
Root Analysis ◽  
Raphson Method

The main purpose of this paper is to obtain the real roots of an expression using the Numerical method, bisection method, Newton's method and secant method. Root analysis is calculated using specific, precise starting points and numerical methods and is represented by Maple. In this research, we used Maple software to analyze the roots of nonlinear equations by special methods, and by showing geometric diagrams, we examined the relevant examples. In this process, the Newton-Raphson method, the algorithm for root access, is fully illustrated by Maple. Also, the secant method and the bisection method were demonstrated by Maple by solving examples and drawing graphs related to each method.

scholarly journals KAJIAN DISTRIBUSI INTENSITAS CAHAYA PADA FENOMENA DIFRAKSI CELAH TUNGGAL DENGAN METODE BAGI DUA DAN METODE NEWTON RAPHSON

2019 ◽  
Vol 4 (2) ◽  
pp. 56-69
Author(s):  
Richard Umbu Datangeji ◽  
Ali Warsito ◽  
Hadi Imam Sutaji ◽  
Laura A. S. Lapono
Keyword(s):  
Light Intensity ◽  
Light Diffraction ◽  
Bisection Method ◽  
Light Intensity Distribution ◽  
Bright Band ◽  
Diffraction Phenomenon ◽  
Left And Right ◽  
Newton Raphson ◽  
Two Peaks ◽  
Raphson Method

Abstrak  Telah dilakukan penelitian tentang distribusi intensitas cahaya pada fenomena difraksi celah tunggal dengan tujuan menerapkan metode Bagi Dua dan metode Newton Raphson untuk memperoleh solusi jarak antara dua titik intensitas dalam fenomena difraksi celah tunggal, menetukan jarak antara dua intensitas pada pita terang, memperoleh grafik distribusi intensitas cahaya terhadap jarak pada kasus difraksi cahaya Franhoufer celah tunggal, serta membandingkan kekonvergenan metode Bagi Dua dan metode Newton Raphson. Solusi jarak antara dua intensitas pada pita terang pada kasus difraksi cahaya Franhoufer celah tunggal diperoleh dengan mencari akar-akar persamaan intensitas cahayanya. Hasil penelitian menunjukan jarak yang semakin besar ketika intensitasnya makin kecil. Ada tiga puncak intensitas, yang pertama puncak untuk intensitas maksimum pada terang pusat yang berada pada jarak 0 cm dan dua puncak untuk terang pertama setelah terang pusat yang mana intensitasnya tinggal 0.05I0 dan berada pada jarak 0.154875 cm sebelah kiri dan sebelah kanan dari intensitas maksimum. Grafik antara jarak dengan perbandingan intensitas terhadap terang maksimum berbentuk sinusoidal, terdapat tiga puncak intensitas. Puncak pertama menunjukan intensitas maksimum yang terdapat pada pita terang pusat dan dua puncak dengan intensitas 0.05I0  yang berada pita terang pertama. Pada kasus ini diperoleh hasil bahwa metode Newton Raphson lebih cepat konvergen dari metode Bagi Dua karena hanya memerlukan 4 iterasi untuk memperoleh solusi, sedangkan metode Bagi Dua membutuhkan 20 iterasi. Metode Newton Raphson juga memiliki nilai error pendekatan lebih kecil dari metode Bagi Dua yaitu 6.43929 x 10-13 sampai 7.52642 x 10-7 sedangkan metode Bagi Dua 1.90735 x 10-6. Abstract  Research on the distribution of light intensity in the phenomenon of single slit diffraction has been carried out with the aim of applying the Bisection method and the Newton Raphson method to obtain a solution between two points in a single slit diffraction phenomenon, determining the distance between two point of intensity in the bright band, obtaining a graph of the light intensity distribution to distance in the case of Franhoufer single slit light diffraction, and comparing the speed of convergence of the Bisection method and the Newton Raphson method. The solution of the distance between two intensities in the bright band in the case of Franhoufer light diffraction in a single slit obtained by looking for the roots of the light intensity equation. The results of the study show that the greater the distance when then intensity gets smaller. There are three peak intensities, the first peak for the highest intensity in the central bright band which is located at a distance of 0 cm and two peaks in the first bright with the intensity is 0.05I0 and is 0.154875 cm left and right of the maximum intensity. The graph between the distance and intensity ratio is sinusoidal, which is three peak intensities. The first peak shows the highest intensity in the central bright band and the two peaks with the intensity of 0.05I0 which is the first bright band. In this case the results of the Newton Raphson method are converged faster than the method of Bisection because it only requires 4 iterations to obtain a solution, while the Bisection method requires 20 iterations. The Newton Raphson method also has a smaller error value than the Bisection method, which is 6.43929 x 10-13 to 7.52642 x 10-6 when the Bisection method is 1.90735 x 10-6.

Approaching quadratic equations from a right angle

2017 ◽  
Vol 101 (552) ◽  
pp. 424-438
Author(s):  
King-Shun Leung
Keyword(s):  
Secondary School ◽  
Mathematics Curriculum ◽  
Quadratic Equation ◽  
Bisection Method ◽  
Quadratic Formula ◽  
Secondary School Mathematics ◽  
Quadratic Equations ◽  
Newton Raphson ◽  
Raphson Method ◽  
Comprehensive Discussion

The theory of quadratic equations (with real coefficients) is an important topic in the secondary school mathematics curriculum. Usually students are taught to solve a quadratic equation ax2 + bx + c = 0 (a ≠ 0) algebraically (by factorisation, completing the square, quadratic formula), graphically (by plotting the graph of the quadratic polynomial y = ax2 + bx + c to find the x-intercepts, if any), and numerically (by the bisection method or Newton-Raphson method). Less well-known is that we can indeed solve a quadratic equation geometrically (by geometric construction tools such as a ruler and compasses, R&C for short). In this article we describe this approach. A more comprehensive discussion on geometric approaches to quadratic equations can be found in [1]. We have also gained much insight from [2] to develop our methods. The tool we use is a set square rather than the more common R&C. But the methods to be presented here can also be carried out with R&C. We choose a set square because it is more convenient (one tool is used instead of two).

scholarly journals A NEW SECOND ORDER DERIVATIVE FREE METHOD FOR NUMERICAL SOLUTION OF NON-LINEAR ALGEBRAIC AND TRANSCENDENTAL EQUATIONS USING INTERPOLATION TECHNIQUE

2021 ◽  
Vol 16 (4) ◽  
Author(s):  
Sanaullah Jamali
Keyword(s):  
Numerical Analysis ◽  
Numerical Solution ◽  
Bisection Method ◽  
Derivative Free ◽  
Interpolation Technique ◽  
Derivative Free Method ◽  
Newton Raphson ◽  
Transcendental Equations ◽  
Regula Falsi Method ◽  
Raphson Method

Its most important task in numerical analysis to find roots of nonlinear equations, several methods already exist in literature to find roots but in this paper, we introduce a unique idea by using the interpolation technique. The proposed method derived from the newton backward interpolation technique and the convergence of the proposed method is quadratic, all types of problems (taken from literature) have been solved by this method and compared their results with another existing method (bisection method (BM), regula falsi method (RFM), secant method (SM) and newton raphson method (NRM)) it’s observed that the proposed method have fast convergence. MATLAB/C++ software is used to solve problems by different methods.

scholarly journals PERBANDINGAN KEEFISIENAN METODE NEWTON-RAPHSON, METODE SECANT, DAN METODE BISECTION DALAM MENGESTIMASI IMPLIED VOLATILITIES SAHAM

2016 ◽  
Vol 5 (1) ◽  
pp. 1
Author(s):  
IDA AYU EGA RAHAYUNI ◽  
KOMANG DHARMAWAN ◽  
LUH PUTU IDA HARINI
Keyword(s):  
Implied Volatility ◽  
Life Time ◽  
Market Mechanism ◽  
Bisection Method ◽  
Stock Volatility ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Newton Raphson ◽  
Real Market ◽  
Raphson Method

Black-Scholes model suggests that volatility is constant or fixed during the life time of the option certainly known. However, this does not fit with what happen in the real market. Therefore, the volatility has to be estimated. Implied Volatility is the etimated volatility from a market mechanism that is considered as a reasonable way to assess the volatility's value. This study was aimed to compare the Newton-Raphson, Secant, and Bisection method, in estimating the stock volatility value of PT Telkom Indonesia Tbk (TLK). It found that the three methods have the same Implied Volatilities, where Newton-Raphson method gained roots more rapidly than the two others, and it has the smallest relative error greater than Secant and Bisection methods.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

A Generalized Compositional Approach for Reservoir Simulation

1983 ◽  
Vol 23 (05) ◽  
pp. 727-742 ◽  
Author(s):  
Larry C. Young ◽  
Robert E. Stephenson
Keyword(s):  
Enhanced Recovery ◽  
Gas Condensate ◽  
Reservoir Modeling ◽  
Pressure Equation ◽  
Compositional Modeling ◽  
Fluid Property ◽  
Black Oil ◽  
Fluid Properties ◽  
Newton Raphson ◽  
Raphson Method

A procedure for solving compositional model equations is described. The procedure is based on the Newton Raphson iteration method. The equations and unknowns in the algorithm are ordered in such a way that different fluid property correlations can be accommodated leadily. Three different correlations have been implemented with the method. These include simplified correlations as well as a Redlich-Kwong equation of state (EOS). The example problems considered area conventional waterflood problem,displacement of oil by CO, andthe displacement of a gas condensate by nitrogen. These examples illustrate the utility of the different fluid-property correlations. The computing times reported are at least as low as for other methods that are specialized for a narrower class of problems. Introduction Black-oil models are used to study conventional recovery techniques in reservoirs for which fluid properties can be expressed as a function of pressure and bubble-point pressure. Compositional models are used when either the pressure. Compositional models are used when either the in-place or injected fluid causes fluid properties to be dependent on composition also. Examples of problems generally requiring compositional models are primary production or injection processes (such as primary production or injection processes (such as nitrogen injection) into gas condensate and volatile oil reservoirs and (2) enhanced recovery from oil reservoirs by CO or enriched gas injection. With deeper drilling, the frequency of gas condensate and volatile oil reservoir discoveries is increasing. The drive to increase domestic oil production has increased the importance of enhanced recovery by gas injection. These two factors suggest an increased need for compositional reservoir modeling. Conventional reservoir modeling is also likely to remain important for some time. In the past, two separate simulators have been developed and maintained for studying these two classes of problems. This result was dictated by the fact that compositional models have generally required substantially greater computing time than black-oil models. This paper describes a compositional modeling approach paper describes a compositional modeling approach useful for simulating both black-oil and compositional problems. The approach is based on the use of explicit problems. The approach is based on the use of explicit flow coefficients. For compositional modeling, two basic methods of solution have been proposed. We call these methods "Newton-Raphson" and "non-Newton-Raphson" methods. These methods differ in the manner in which a pressure equation is formed. In the Newton-Raphson method the iterative technique specifies how the pressure equation is formed. In the non-Newton-Raphson method, the composition dependence of certain ten-ns is neglected to form the pressure equation. With the non-Newton-Raphson pressure equation. With the non-Newton-Raphson methods, three to eight iterations have been reported per time step. Our experience with the Newton-Raphson method indicates that one to three iterations per tune step normally is sufficient. In the present study a Newton-Raphson iteration sequence is used. The calculations are organized in a manner which is both efficient and for which different fluid property descriptions can be accommodated readily. Early compositional simulators were based on K-values that were expressed as a function of pressure and convergence pressure. A number of potential difficulties are inherent in this approach. More recently, cubic equations of state such as the Redlich-Kwong, or Peng-Robinson appear to be more popular for the correlation Peng-Robinson appear to be more popular for the correlation of fluid properties. SPEJ p. 727

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