**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**288

# Search results for: Newton- Cotes formula

##### 288 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.

##### 287 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.

##### 286 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.

##### 285 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.

##### 284 Dynamic Analysis by a Family of Time Marching Procedures Based On Numerically Computed Green’s Functions

**Authors:**
Delfim Soares Jr.

**Abstract:**

In this work, a new family of time marching procedures based on Green’s function matrices is presented. The formulation is based on the development of new recurrence relationships, which employ time integral terms to treat initial condition values. These integral terms are numerically evaluated taking into account Newton-Cotes formulas. The Green’s matrices of the model are also numerically computed, taking into account the generalized-α method and subcycling techniques. As it is discussed and illustrated along the text, the proposed procedure is efficient and accurate, providing a very attractive time marching technique.

**Keywords:**
Dynamics,
Time-Marching,
Green’s Function,
Generalized-α Method,
Subcycling.

##### 283 Improvement of Gregory's formula using Particle Swarm Optimization

**Authors:**
N. Khelil. L. Djerou ,
A. Zerarka,
M. Batouche

**Abstract:**

**Keywords:**
Numerical integration,
Gregory Formula,
Particle Swarm optimization.

##### 282 Developing a Simple and an Accurate Formula for the Conduction Angle of a Single Phase Rectifier with RL Load

**Authors:**
S. Ali Al-Mawsawi,
Fadhel A. Albasri

**Abstract:**

**Keywords:**
Conduction Angle,
Firing Angle,
Excitation Angle,
Load Angle.

##### 281 Flow Properties of Commercial Infant Formula Powders

**Authors:**
Maja Benkovic,
Ingrid Bauman

**Abstract:**

**Keywords:**
flow properties,
infant formula,
powderedmaterial

##### 280 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.

##### 279 All Proteins Have a Basic Molecular Formula

**Authors:**
Homa Torabizadeh

**Abstract:**

**Keywords:**
Protein molecular formula,
Basic unit formula,
Protparam tool.

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

**Authors:**
Talib Hashim Hasan

**Abstract:**

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

##### 277 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.

##### 276 Establishing a New Simple Formula for Buckling Length Factor (K) of Rigid Frames Columns

**Authors:**
Ehab Hasan Ahmed Hasan Ali

**Abstract:**

**Keywords:**
Buckling length,
New formula,
Curve fitting,
Simplification,
Steel column design.

##### 275 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.

##### 274 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.

##### 273 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.

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

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

**Abstract:**

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

##### 271 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.

##### 270 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.

##### 269 An Asymptotic Formula for Pricing an American Exchange Option

**Authors:**
Hsuan-Ku Liu

**Abstract:**

In this paper, the American exchange option (AEO) valuation problem is modelled as a free boundary problem. The critical stock price for an AEO is satisfied an integral equation implicitly. When the remaining time is large enough, an asymptotic formula is provided for pricing an AEO. The numerical results reveal that our asymptotic pricing formula is robust and accurate for the long-term AEO.

**Keywords:**
Integral equation,
asymptotic solution,
free boundary problem,
American exchange option.

##### 268 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.

##### 267 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.

##### 266 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.

##### 265 Parallel Block Backward Differentiation Formulas for Solving Ordinary Differential Equations

**Authors:**
Khairil Iskandar Othman,
Zarina Bibi Ibrahim,
Mohamed Suleiman

**Abstract:**

**Keywords:**
Backward Differentiation Formula,
block,
ordinarydifferential equations.

##### 264 Direct Block Backward Differentiation Formulas for Solving Second Order Ordinary Differential Equations

**Authors:**
Zarina Bibi Ibrahim,
Mohamed Suleiman,
Khairil Iskandar Othman

**Abstract:**

**Keywords:**
Backward Differentiation Formula,
block,
secondorder.

##### 263 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.

##### 262 Implementation of the Recursive Formula for Evaluation of the Strength of Daniels’ Model

**Authors:**
Václav Sadílek,
Miroslav Vořechovský

**Abstract:**

**Keywords:**
Daniels bundle model,
equal load sharing,
Python,
mpmath.

##### 261 The Frame Analysis and Testing for Student Formula

**Authors:**
Tanawat Limwathanagura,
Chartree Sithananun,
Teekayu Limchamroon,
Thanyarat Singhanart

**Abstract:**

The objective of this paper is to study the analysis and testing for determining the torsional stiffness of the student formula-s space frame. From past study, the space frame for Chulalongkorn University Student Formula team used in 2011 TSAE Auto Challenge Student Formula in Thailand was designed by considering required mass and torsional stiffness based on the numerical method and experimental method. The numerical result was compared with the experimental results to verify the torsional stiffness of the space frame. It can be seen from the large error of torsional stiffness of 2011 frame that the experimental result can not verify by the numerical analysis due to the different between the numerical model and experimental setting. In this paper, the numerical analysis and experiment of the same 2011 frame model is performed by improving the model setting. The improvement of both numerical analysis and experiment are discussed to confirm that the models from both methods are same. After the frame was analyzed and tested, the results are compared to verify the torsional stiffness of the frame. It can be concluded that the improved analysis and experiments can used to verify the torsional stiffness of the space frame.

**Keywords:**
Space Frame,
Student Formula,
Torsional Stiffness,
TSAE Auto Challenge

##### 260 The Development of Chulalongkorn University's SAE Student Formula's Space Frame

**Authors:**
Chartree Sithananun,
Teekayu Limchamroon,
Tanawat Limwathanagura,
Thanyarat Singhanart

**Abstract:**

**Keywords:**
SAE Student Formula,
Space Frame,
Torsional
Stiffness

##### 259 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.