scholarly journals PERBANDINGAN SOLUSI SISTEM PERSAMAAN NONLINEAR MENGGUNAKAN METODE NEWTON-RAPHSON DAN METODE JACOBIAN

2013 ◽  
Vol 2 (2) ◽  
pp. 11
Author(s):  
NANDA NINGTYAS RAMADHANI UTAMI ◽  
I NYOMAN WIDANA ◽  
NI MADE ASIH
Keyword(s):  
Nonlinear Equations ◽  
Iteration Method ◽  
Initial Point ◽  
Iteration Process ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Newton Raphson ◽  
Raphson Method

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.

scholarly journals A New Second-Order Iteration Method for Solving Nonlinear Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Shin Min Kang ◽  
Arif Rafiq ◽  
Young Chel Kwun
Keyword(s):  
Nonlinear Equations ◽  
Iteration Method ◽  
Nonlinear Operator ◽  
Efficiency Index ◽  
Second Order ◽  
First Order ◽  
Newton Raphson ◽  
Second Order Convergence ◽  
Derivatives Of ◽  
Raphson Method

We establish a new second-order iteration method for solving nonlinear equations. The efficiency index of the method is 1.4142 which is the same as the Newton-Raphson method. By using some examples, the efficiency of the method is also discussed. It is worth to note that (i) our method is performing very well in comparison to the fixed point method and the method discussed in Babolian and Biazar (2002) and (ii) our method is so simple to apply in comparison to the method discussed in Babolian and Biazar (2002) and involves only first-order derivative but showing second-order convergence and this is not the case in Babolian and Biazar (2002), where the method requires the computations of higher-order derivatives of the nonlinear operator involved in the functional equation.

A Numerical Simulation on the Effect of Vaccination and Treatments for the Fractional Hepatitis B Model

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
Haile Habenom ◽  
D. L. Suthar ◽  
D. Baleanu ◽  
S. D. Purohit
Keyword(s):  
Hepatitis B ◽  
Nonlinear Equations ◽  
Control Strategies ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
B Virus ◽  
The Stability ◽  
Hbv Model ◽  
Raphson Method ◽  
Jacobi Collocation Method

Abstract The aim of this paper is to develop a fractional order mathematical model for describing the spread of hepatitis B virus (HBV). We also provide a rigorous mathematical analysis of the stability of the disease-free equilibrium (DFE) and the endemic equilibrium of the system based on the basic reproduction number. Here, the infectious disease HBV model is described mathematically in a nonlinear system of differential equations in a caputo sense, and hence, Jacobi collocation method is used to reduce into a system of nonlinear equations. Finally, Newton Raphson method is used for the systems of nonlinear equations to arrive at an approximate solution and matlab 2018 has helped us to simulate the nature of each compartment and effects of the possible control strategies (i.e., vaccination and isolation).

scholarly journals Application of newton Raphson and steepest descent method for precise positioning for mobile communications

2018 ◽  
Vol 7 (2.7) ◽  
pp. 237
Author(s):  
Ch Yamini Surya Teja ◽  
B Vijay Gopal Reddy ◽  
S Sri Harsha ◽  
K Uday Kiran ◽  
Dr S.Koteswara Rao
Keyword(s):  
Mobile Communications ◽  
Initial Point ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Band Frequency ◽  
Precise Position ◽  
Sensor Position ◽  
Newton Raphson ◽  
Network Technologies ◽  
Derivatives Of

GSM is a wireless networksystem. GSM mostly uses TDMA and most uses three digital wirelessmobile network technologies to compresses data, sends by using a channel along with other samples of data, in different time slots. It makes use of 900 to 1800MHz band frequency for transmission. Very accurate and exact wireless algorithms are difficult in all environmental conditions. Wireless communications use various parametric measurements to determine the sensor position. TOA is the time taken by the signal from source to reach the receiver’s position. Newton Raphson method is an iterative numerical method uses partial derivatives of a functions or a system of equations in a suitable search direction. Newton Raphson consider two fundamental arguments: The first one is considering a good starting or initial point which is approximate to the solution and the secondary thing is to consider a distinguishable error which plays important role on approximation of the solution. In the present work, the Newton Raphson algorithm is implemented to obtain precise position of the receiver.

scholarly journals Hybrid Method with Perturbation for Lipschitzian Pseudocontractions

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen
Keyword(s):  
Nonlinear Operator ◽  
Real Hilbert Space ◽  
Initial Point ◽  
Nonempty Closed Convex Subset ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Hybrid Steepest Descent Method ◽  
Arbitrary Initial Point ◽  
Mann’S Iteration ◽  
Fixed Point Sets

Assume thatFis a nonlinear operator which is Lipschitzian and strongly monotone on a nonempty closed convex subsetCof a real Hilbert spaceH. Assume also thatΩis the intersection of the fixed point sets of a finite number of Lipschitzian pseudocontractive self-mappings onC. By combining hybrid steepest-descent method, Mann’s iteration method and projection method, we devise a hybrid iterative algorithm with perturbationF, which generates two sequences from an arbitrary initial pointx0∈H. These two sequences are shown to converge in norm to the same pointPΩx0under very mild assumptions.

scholarly journals On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
H. Montazeri ◽  
F. Soleymani ◽  
S. Shateyi ◽  
S. S. Motsa
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
The Other ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Numerical Tests ◽  
Programming Package ◽  
New Iterative Method

We consider a system of nonlinear equationsF(x)=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.

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.

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