Abstract: Taking into account that many problems of natural
sciences and engineering are reduced to solving initial-value problem
for ordinary differential equations, beginning from Newton, the
scientists investigate approximate solution of ordinary differential
equations. There are papers of different authors devoted to the
solution of initial value problem for ODE. The Euler-s known
method that was developed under the guidance of the famous
scientists Adams, Runge and Kutta is the most popular one among
these methods.
Recently the scientists began to construct the methods preserving
some properties of Adams and Runge-Kutta methods and called them
hybrid methods. The constructions of such methods are investigated
from the middle of the XX century. Here we investigate one
generalization of multistep and hybrid methods and on their base we
construct specific methods of accuracy order p = 5 and p = 6 for
k = 1 ( k is the order of the difference method).
Abstract: Combined conduction-free convection heat transfer in
vertical eccentric annuli is numerically investigated using a finitedifference
technique. Numerical results, representing the heat transfer
parameters such as annulus walls temperature, heat flux, and heat
absorbed in the developing region of the annulus, are presented for a
Newtonian fluid of Prandtl number 0.7, fluid-annulus radius ratio 0.5,
solid-fluid thermal conductivity ratio 10, inner and outer wall
dimensionless thicknesses 0.1 and 0.2, respectively, and
dimensionless eccentricities 0.1, 0.3, 0.5, and 0.7. The annulus walls
are subjected to thermal boundary conditions, which are obtained by
heating one wall isothermally whereas keeping the other wall at inlet
fluid temperature. In the present paper, the annulus heights required
to achieve thermal full development for prescribed eccentricities are
obtained. Furthermore, the variation in the height of thermal full
development as function of the geometrical parameter, i.e.,
eccentricity is also investigated.
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.
Abstract: The relationship between different types of Molybdenum disulfide greases under extreme pressure loading and different speed situations have been studied using Design of Experiment (DOE) under 1200rpm steady state rotational speed and cyclic frequencies between 2400 and 1200rpm using a Plint machine software to set up the different rotational speed situations.
Research described here is aimed at providing good friction and wear performance while optimizing cyclic frequencies and MoS2 concentration due to the recent concern about grease behavior in extreme pressure applications. Extreme load of 785 Newton was used in conjunction with different cyclic frequencies (2400rpm -3.75min, 1200rpm -7.5min, 2400rpm -3.75min, 1200rpm -7.5min), to examine lithium based grease with and without MoS2 for equal number of revolutions, and a total run of 36000 revolutions; then compared to 1200rpm steady speed for the same total number of revolutions. 4 Ball wear tester was utilized to run large number of experiments randomly selected by the DOE software. The grease was combined with fine grade MoS2 or technical grade then heated to 750C and the wear scar width was collected at the end of each test. DOE model validation results verify that the data were very significant and can be applied to a wide range of extreme pressure applications. Based on simulation results and Scanning Electron images (SEM), it has been found that wear was largely dependent on the cyclic frequency condition. It is believed that technical grade MoS2 greases under faster cyclic speeds perform better and provides antiwear film that can resist extreme pressure loadings. Figures showed reduced wear scars width and improved frictional values.
Abstract: The electrical interaction between two axisymmetric
spheroidal particles in an electrolyte solution is examined numerically.
A Galerkin finite element method combined with a Newton-Raphson
iteration scheme is proposed to evaluate the spatial variation in the
electrical potential, and the result obtained used to estimate the
interaction energy between two particles. We show that if the surface
charge density is fixed, the potential gradient is larger at a point, which
has a larger curvature, and if surface potential is fixed, surface charge
density is proportional to the curvature. Also, if the total interaction
energy against closest surface-to-surface curve exhibits a primary
maximum, the maximum follows the order (oblate-oblate) >
(sphere-sphere)>(oblate-prolate)>(prolate-prolate), and if the curve
has a secondary minimum, the absolute value of the minimum follows
the same order.
Abstract: The aim of this paper is to investigate twodimensional unsteady flow of a viscous incompressible fluid about stagnation point on permeable stretching sheet in presence of time dependent free stream velocity. Fluid is considered in the influence of transverse magnetic field in the presence of radiation effect. Rosseland approximation is use to model the radiative heat transfer. Using time-dependent stream function, partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by using Runge-Kutta Fehlberg method with the help of Newton-Raphson shooting technique. In the present work the effect of unsteadiness parameter, magnetic field parameter, radiation parameter, stretching parameter and the Prandtl number on flow and heat transfer characteristics have been discussed. Skin-friction coefficient and Nusselt number at the sheet are computed and discussed. The results reported in the paper are in good agreement with published work in literature by other researchers.
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.
Abstract: This paper made an attempt to investigate the problem associated with enhancement of emulsions of light crude oil-water recovery in an oil field of Algerian Sahara. Measurements were taken through experiments using RheoStress (RS600). Factors such as shear rate, temperature and light oil concentration on the viscosity behavior were considered. Experimental measurements were performed in terms of shear stress–shear rate, yield stress and flow index on mixture of light crude oil–water. The rheological behavior of emulsion showed Non-Newtonian shear thinning behavior (Herschel-Bulkley). The experiments done in the laboratory showed the stability of some water in light crude oil emulsions form during consolidate oil recovery process. To break the emulsion using additives may involve higher cost and could be very expensive. Therefore, further research should be directed to find solution of these problems that have been encountered.
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.
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.
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.
Abstract: Newton-Raphson State Estimation method using bus
admittance matrix remains as an efficient and most popular method to
estimate the state variables. Elements of Jacobian matrix are computed
from standard expressions which lack physical significance. In this
paper, elements of the state estimation Jacobian matrix are obtained
considering the power flow measurements in the network elements.
These elements are processed one-by-one and the Jacobian matrix H is
updated suitably in a simple manner. The constructed Jacobian matrix
H is integrated with Weight Least Square method to estimate the state
variables. The suggested procedure is successfully tested on IEEE
standard systems.
Abstract: This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.
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.
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.
Abstract: The seismic response of steel shear wall system considering nonlinearity effects using finite element method is investigated in this paper. The non-linear finite element analysis has potential as usable and reliable means for analyzing of civil structures with the availability of computer technology. In this research the large displacements and materially nonlinear behavior of shear wall is presented with developing of finite element code. A numerical model based on the finite element method for the seismic analysis of shear wall is presented with developing of finite element code in this research. To develop the finite element code, the standard Galerkin weighted residual formulation is used. Two-dimensional plane stress model and total Lagrangian formulation was carried out to present the shear wall response and the Newton-Raphson method is applied for the solution of nonlinear transient equations. The presented model in this paper can be developed for analysis of civil engineering structures with different material behavior and complicated geometry.
Abstract: Solving Ordinary Differential Equations (ODEs) by
using Partitioning Block Intervalwise (PBI) technique is our aim in
this paper. The PBI technique is based on Block Adams Method and
Backward Differentiation Formula (BDF). Block Adams Method
only use the simple iteration for solving while BDF requires Newtonlike
iteration involving Jacobian matrix of ODEs which consumes a
considerable amount of computational effort. Therefore, PBI is
developed in order to reduce the cost of iteration within acceptable
maximum error
Abstract: A new Meta heuristic approach called "Randomized gravitational emulation search algorithm (RGES)" for solving vertex covering problems has been designed. This algorithm is found upon introducing randomization concept along with the two of the four primary parameters -velocity- and -gravity- in physics. A new heuristic operator is introduced in the domain of RGES to maintain feasibility specifically for the vertex covering problem to yield best solutions. The performance of this algorithm has been evaluated on a large set of benchmark problems from OR-library. Computational results showed that the randomized gravitational emulation search algorithm - based heuristic is capable of producing high quality solutions. The performance of this heuristic when compared with other existing heuristic algorithms is found to be excellent in terms of solution quality.
Abstract: In this paper, based on steady-state models of Flexible
AC Transmission System (FACTS) devices, the sizing of static
synchronous series compensator (SSSC) controllers in transmission
network is formed as an optimization problem. The objective of this
problem is to reduce the transmission losses in the network. The
optimization problem is solved using particle swarm optimization
(PSO) technique. The Newton-Raphson load flow algorithm is
modified to consider the insertion of the SSSC devices in the
network. A numerical example, illustrating the effectiveness of the
proposed algorithm, is introduced. In addition, a novel model of a 3-
phase voltage source converter (VSC) that is suitable for series
connected FACTS a controller is introduced. The model is verified
by simulation using Power System Blockset (PSB) and Simulink
software.
Abstract: A considerable progress has been achieved in transient
stability analysis (TSA) with various FACTS controllers. But, all
these controllers are associated with single transmission line. This
paper is intended to discuss a new approach i.e. a multi-line FACTS
controller which is interline power flow controller (IPFC) for TSA of
a multi-machine power system network. A mathematical model of
IPFC, termed as power injection model (PIM) presented and this
model is incorporated in Newton-Raphson (NR) power flow
algorithm. Then, the reduced admittance matrix of a multi-machine
power system network for a three phase fault without and with IPFC
is obtained which is required to draw the machine swing curves. A
general approach based on L-index has also been discussed to find
the best location of IPFC to reduce the proximity to instability of a
power system. Numerical results are carried out on two test systems
namely, 6-bus and 11-bus systems. A program in MATLAB has
been written to plot the variation of generator rotor angle and speed
difference curves without and with IPFC for TSA and also a simple
approach has been presented to evaluate critical clearing time for test
systems. The results obtained without and with IPFC are compared
and discussed.