**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**8105

# Search results for: Newton's method

##### 8105 New Newton's Method with Third-order Convergence for Solving Nonlinear Equations

**Authors:**
Osama Yusuf Ababneh

**Abstract:**

For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

**Keywords:**
Third-order convergence,
non-linear equations,
root finding,
iterative method.

##### 8104 A New Method to Solve a Non Linear Differential System

**Authors:**
Seifedine Kadry

**Abstract:**

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

**Keywords:**
Continuation Method,
Newton Method,
Finite Difference Method,
Numerical Analysis and Non-Linear partial Differential Equation.

##### 8103 An Efficient Method for Solving Multipoint Equation Boundary Value Problems

**Authors:**
Ampon Dhamacharoen,
Kanittha Chompuvised

**Abstract:**

**Keywords:**
Boundary value problem; Multipoint equation
boundary value problems,
Shooting Method,
Newton-Broyden
method.

##### 8102 The Application of Homotopy Method In Solving Electrical Circuit Design Problem

**Authors:**
Talib Hashim Hasan

**Abstract:**

**Keywords:**
electrical circuit homotopy,
methods,
MATLAB,
Newton homotopy

##### 8101 A Contractor Iteration Method Using Eigenpairs for Positive Solutions of Nonlinear Elliptic Equation

**Authors:**
Hailong Zhu,
Zhaoxiang Li,
Kejun Zhuang

**Abstract:**

By means of Contractor Iteration Method, we solve and visualize the Lane-Emden(-Fowler) equation Δu + up = 0, in Ω, u = 0, on ∂Ω. It is shown that the present method converges quadratically as Newton’s method and the computation of Contractor Iteration Method is cheaper than the Newton’s method.

**Keywords:**
Positive solutions,
newton's method,
contractor iteration method,
Eigenpairs.

##### 8100 Comparison of Newton Raphson and Gauss Seidel Methods for Power Flow Analysis

**Authors:**
H. Abaali,
T. Talbi,
R.Skouri

**Abstract:**

This paper presents a comparative study of the Gauss Seidel and Newton-Raphson polar coordinates methods for power flow analysis. The effectiveness of these methods are evaluated and tested through a different IEEE bus test system on the basis of number of iteration, computational time, tolerance value and convergence.

**Keywords:**
Convergence time,
Gauss-Seidel Method,
Newton-Raphson Method,
number of iteration,
power flow analysis.

##### 8099 Approximated Solutions of Two-Point Nonlinear Boundary Problem by a Combination of Taylor Series Expansion and Newton Raphson Method

**Authors:**
Chinwendu. B. Eleje,
Udechukwu P. Egbuhuzor

**Abstract:**

One of the difficulties encountered in solving nonlinear Boundary Value Problems (BVP) by many researchers is finding approximated solutions with minimum deviations from the exact solutions without so much rigor and complications. In this paper, we propose an approach to solve a two point BVP which involves a combination of Taylor series expansion method and Newton Raphson method. Furthermore, the fourth and sixth order approximated solutions are obtained and we compare their relative error and rate of convergence to the exact solution. Finally, some numerical simulations are presented to show the behavior of the solution and its derivatives.

**Keywords:**
Newton Raphson method,
non-linear boundary value problem,
Taylor series approximation,
Michaelis-Menten equation.

##### 8098 Fast and Efficient Algorithms for Evaluating Uniform and Nonuniform Lagrange and Newton Curves

**Authors:**
Taweechai Nuntawisuttiwong,
Natasha Dejdumrong

**Abstract:**

**Keywords:**
Newton interpolation,
Lagrange interpolation,
linear
complexity.

##### 8097 Newton-Raphson State Estimation Solution Employing Systematically Constructed Jacobian Matrix

**Authors:**
Nursyarizal Mohd Nor,
Ramiah Jegatheesan,
Perumal Nallagownden

**Abstract:**

**Keywords:**
State Estimation (SE),
Weight Least Square (WLS),
Newton-Raphson State Estimation (NRSE),
Jacobian matrix H.

##### 8096 A Fully Implicit Finite-Difference Solution to One Dimensional Coupled Nonlinear Burgers’ Equations

**Authors:**
Vineet K. Srivastava,
Mukesh K. Awasthi,
Mohammad Tamsir

**Abstract:**

A fully implicit finite-difference method has been proposed for the numerical solutions of one dimensional coupled nonlinear Burgers’ equations on the uniform mesh points. The method forms a system of nonlinear difference equations which is to be solved at each iteration. Newton’s iterative method has been implemented to solve this nonlinear assembled system of equations. The linear system has been solved by Gauss elimination method with partial pivoting algorithm at each iteration of Newton’s method. Three test examples have been carried out to illustrate the accuracy of the method. Computed solutions obtained by proposed scheme have been compared with analytical solutions and those already available in the literature by finding L2 and L∞ errors.

**Keywords:**
Burgers’ equation,
Implicit Finite-difference method,
Newton’s method,
Gauss elimination with partial pivoting.

##### 8095 Iteration Acceleration for Nonlinear Coupled Parabolic-Hyperbolic System

**Authors:**
Xia Cui,
Guang-wei Yuan,
Jing-yan Yue

**Abstract:**

A Picard-Newton iteration method is studied to accelerate the numerical solution procedure of a class of two-dimensional nonlinear coupled parabolic-hyperbolic system. The Picard-Newton iteration is designed by adding higher-order terms of small quantity to an existing Picard iteration. The discrete functional analysis and inductive hypothesis reasoning techniques are used to overcome difficulties coming from nonlinearity and coupling, and theoretical analysis is made for the convergence and approximation properties of the iteration scheme. The Picard-Newton iteration has a quadratic convergent ratio, and its solution has second order spatial approximation and first order temporal approximation to the exact solution of the original problem. Numerical tests verify the results of the theoretical analysis, and show the Picard-Newton iteration is more efficient than the Picard iteration.

**Keywords:**
Nonlinearity,
iterative acceleration,
coupled parabolic hyperbolic system,
quadratic convergence,
numerical analysis.

##### 8094 Numerical Analysis of Thermal Conductivity of Non-Charring Material Ablation Carbon-Carbon and Graphite with Considering Chemical Reaction Effects, Mass Transfer and Surface Heat Transfer

**Authors:**
H. Mohammadiun,
A. Kianifar,
A. Kargar

**Abstract:**

**Keywords:**
Ablation rate,
surface recession,
interior temperaturedistribution,
non charring material ablation,
Newton Rafson method.

##### 8093 An Implicit Methodology for the Numerical Modeling of Locally Inextensible Membranes

**Authors:**
Aymen Laadhari

**Abstract:**

**Keywords:**
Finite element method,
Newton method,
level set,
Navier-Stokes,
inextensible membrane,
liquid drop.

##### 8092 Numerical Study of a Class of Nonlinear Partial Differential Equations

**Authors:**
Kholod M. Abu-Alnaja

**Abstract:**

**Keywords:**
Crank-Nicolson Scheme,
Douglas Scheme,
Partial
Differential Equations

##### 8091 Spline Collocation for Solving System of Fredholm and Volterra Integral Equations

**Authors:**
N. Ebrahimi,
J. Rashidinia

**Abstract:**

In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.

**Keywords:**
Convergence analysis,
Cubic B-spline,
Newton-
Cotes formula,
System of Fredholm and Volterra integral equations.

##### 8090 Implicit Eulerian Fluid-Structure Interaction Method for the Modeling of Highly Deformable Elastic Membranes

**Authors:**
Aymen Laadhari,
Gábor Székely

**Abstract:**

**Keywords:**
Fluid-membrane interaction,
stretching,
Eulerian,
finite element method,
Newton,
implicit.

##### 8089 Cantor Interpolating Spline to Design Electronic Mail Boxes

**Authors:**
Adil Al-Rammahi

**Abstract:**

Electronic mail is very important in present time. Many researchers work for designing, improving, securing, fasting, goodness and others fields in electronic mail. This paper introduced new algorithm to use Cantor sets and cubic spline interpolating function in the electronic mail design. Cantor sets used as the area (or domain) of the mail, while spline function used for designing formula. The roots of spline function versus Cantor sets used as the controller admin. The roots calculated by the numerical Newton – Raphson's method. The result of this algorithm was promised.

**Keywords:**
Cantor sets,
spline,
electronic mail design,
Newton – Raphson's method.

##### 8088 A Special Algorithm to Approximate the Square Root of Positive Integer

**Authors:**
Hsian Ming Goo

**Abstract:**

The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

**Keywords:**
Special approximate algorithm,
square root,
Pell’s
equation,
Newton’s method,
error analysis.

##### 8087 Power Flow Control with UPFC in Power Transmission System

**Authors:**
Samina Elyas Mubeen,
R. K. Nema,
Gayatri Agnihotri

**Abstract:**

**Keywords:**
Newton-Raphson algorithm,
Load flow,
Unified
power flow controller,
Voltage source model.

##### 8086 New Laguerre-s Type Method for Solving of a Polynomial Equations Systems

**Authors:**
Oleksandr Poliakov,
Yevgen Pashkov,
Marina Kolesova,
Olena Chepenyuk,
Mykhaylo Kalinin,
Vadym Kramar

**Abstract:**

**Keywords:**
Iterative method,
Laguerre's method,
Newton's
method,
polynomial equation,
system of equations

##### 8085 A TFETI Domain Decompositon Solver for Von Mises Elastoplasticity Model with Combination of Linear Isotropic-Kinematic Hardening

**Authors:**
Martin Cermak,
Stanislav Sysala

**Abstract:**

In this paper we present the efficient parallel implementation of elastoplastic problems based on the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. This approach allow us to use parallel solution and compute this nonlinear problem on the supercomputers and decrease the solution time and compute problems with millions of DOFs. In our approach we consider an associated elastoplastic model with the von Mises plastic criterion and the combination of linear isotropic-kinematic hardening law. This model is discretized by the implicit Euler method in time and by the finite element method in space. We consider the system of nonlinear equations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel by the above mentioned TFETI. The implementation of this problem is realized in our in-house MatSol packages developed in MatLab.

**Keywords:**
Isotropic-kinematic hardening,
TFETI,
domain
decomposition,
parallel solution.

##### 8084 High Performance Computing Using Out-of- Core Sparse Direct Solvers

**Authors:**
Mandhapati P. Raju,
Siddhartha Khaitan

**Abstract:**

**Keywords:**
Out-of-core,
PARDISO,
MUMPS,
Newton.

##### 8083 A Modification on Newton's Method for Solving Systems of Nonlinear Equations

**Authors:**
Jafar Biazar,
Behzad Ghanbari

**Abstract:**

In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

**Keywords:**
System of nonlinear equations.

##### 8082 Bond Graph Modeling of Mechanical Dynamics of an Excavator for Hydraulic System Analysis and Design

**Authors:**
Mutuku Muvengei,
John Kihiu

**Abstract:**

**Keywords:**
Actuators,
bond graphs,
inverse dynamics,
recursive
equations,
quintic polynomial trajectory.

##### 8081 Reentry Trajectory Optimization Based on Differential Evolution

**Authors:**
Songtao Chang,
Yongji Wang,
Lei Liu,
Dangjun Zhao

**Abstract:**

**Keywords:**
reentry vehicle,
trajectory optimization,
constraint optimal,
differential evolution.

##### 8080 Evaluation of Mixed-Mode Stress Intensity Factor by Digital Image Correlation and Intelligent Hybrid Method

**Authors:**
K. Machida,
H. Yamada

**Abstract:**

Displacement measurement was conducted on compact normal and shear specimens made of acrylic homogeneous material subjected to mixed-mode loading by digital image correlation. The intelligent hybrid method proposed by Nishioka et al. was applied to the stress-strain analysis near the crack tip. The accuracy of stress-intensity factor at the free surface was discussed from the viewpoint of both the experiment and 3-D finite element analysis. The surface images before and after deformation were taken by a CMOS camera, and we developed the system which enabled the real time stress analysis based on digital image correlation and inverse problem analysis. The great portion of processing time of this system was spent on displacement analysis. Then, we tried improvement in speed of this portion. In the case of cracked body, it is also possible to evaluate fracture mechanics parameters such as the J integral, the strain energy release rate, and the stress-intensity factor of mixed-mode. The 9-points elliptic paraboloid approximation could not analyze the displacement of submicron order with high accuracy. The analysis accuracy of displacement was improved considerably by introducing the Newton-Raphson method in consideration of deformation of a subset. The stress-intensity factor was evaluated with high accuracy of less than 1% of the error.

**Keywords:**
Digital image correlation,
mixed mode,
Newton-Raphson method,
stress intensity factor.

##### 8079 Time/Temperature-Dependent Finite Element Model of Laminated Glass Beams

**Authors:**
Alena Zemanová,
Jan Zeman,
Michal Šejnoha

**Abstract:**

**Keywords:**
Laminated glass,
finite element method,
finite-strain
Reissner model,
Lagrange multipliers,
generalized Maxwell model,
Williams-Landel-Ferry equation,
Newton method.

##### 8078 Power Flow Analysis for Radial Distribution System Using Backward/Forward Sweep Method

**Authors:**
J. A. Michline Rupa,
S. Ganesh

**Abstract:**

This paper proposes a backward/forward sweep method to analyze the power flow in radial distribution systems. The distribution system has radial structure and high R/X ratios. So the newton-raphson and fast decoupled methods are failed with distribution system. The proposed method presents a load flow study using backward/forward sweep method, which is one of the most effective methods for the load-flow analysis of the radial distribution system. By using this method, power losses for each bus branch and voltage magnitudes for each bus node are determined. This method has been tested on IEEE 33-bus radial distribution system and effective results are obtained using MATLAB.

**Keywords:**
Backward/Forward sweep method,
Distribution
system,
Load flow analysis.

##### 8077 A Quadcopter Stability Analysis: A Case Study Using Simulation

**Authors:**
C. S. Bianca Sabrina,
N. Egidio Raimundo,
L. Alexandre Baratella,
C. H. João Paulo

**Abstract:**

This paper aims to present a study, with the theoretical concepts and applications of the Quadcopter, using the MATLAB simulator. In order to use this tool, the study of the stability of the drone through a Proportional - Integral - Derivative (PID) controller will be presented. After the stability study, some tests are done on the simulator and its results will be presented. From the mathematical model, it is possible to find the Newton-Euler angles, so that it is possible to stabilize the quadcopter in a certain position in the air, starting from the ground. In order to understand the impact of the controllers gain values on the stabilization of the Euler-Newton angles, three conditions will be tested with different controller gain values.

**Keywords:**
Controllers,
drones,
quadcopter,
stability.

##### 8076 Forward Kinematics Analysis of a 3-PRS Parallel Manipulator

**Authors:**
Ghasem Abbasnejad,
Soheil Zarkandi,
Misagh Imani

**Abstract:**

In this article the homotopy continuation method (HCM) to solve the forward kinematic problem of the 3-PRS parallel manipulator is used. Since there are many difficulties in solving the system of nonlinear equations in kinematics of manipulators, the numerical solutions like Newton-Raphson are inevitably used. When dealing with any numerical solution, there are two troublesome problems. One is that good initial guesses are not easy to detect and another is related to whether the used method will converge to useful solutions. Results of this paper reveal that the homotopy continuation method can alleviate the drawbacks of traditional numerical techniques.

**Keywords:**
Forward kinematics,
Homotopy continuationmethod,
Parallel manipulators,
Rotation matrix