scholarly journals A Generalized Regula Falsi Method for Finding Zeros and Extrema of Real Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Abel Gomes ◽  
José Morgado
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
Real Function ◽  
Local Minima ◽  
Intermediate Value Theorem ◽  
Real Functions ◽  
Intermediate Value ◽  
Regula Falsi Method

Many zero-finding numerical methods are based on the Intermediate Value Theorem, which states that a zero of a real function is bracketed in a given interval if and have opposite signs; that is, . But, some zeros cannot be bracketed this way because they do not satisfy the precondition . For example, local minima and maxima that annihilate may not be bracketed by the Intermediate Value Theorem. In this case, we can always use a numerical method for bracketing extrema, checking then whether it is a zero of or not. Instead, this paper introduces a single numerical method, calledgeneralized regula falsi(GRF) method to determine both zeros and extrema of a function. Consequently, it differs from the standardregula falsi methodin that it is capable of finding any function zero in a given interval even when the Intermediate Value Theorem is not satisfied.

Vortex Simulation of Rotor/Stator Interaction in Turbomachinery

1998 ◽  
Author(s):  
Xian Hong Wu ◽  
Mao Zhang Chen
Keyword(s):  
Numerical Methods ◽  
Flow Field ◽  
Diffusion Process ◽  
Numerical Method ◽  
Outer Region ◽  
Vortex Method ◽  
Convective Process ◽  
Rotor Stator Interaction ◽  
Initial Description ◽  
Lagrangian Frame

A new numerical method is presented in this paper to simulate rotor/stator interaction in turbomachinery by use of a vortex method based on a Lagrangian frame. The algorithm takes the result from steady solution as input, which can give an initial description of the unsteady disturbance flow field. To calculate the unsteady response to these disturbances, the Lagrangian vortex method is used to capture the convective process, and the deterministic vortex scheme to approximate the viscous diffusion process. The application of Baldwin-Lomax turbulence model in wakes is developed, so as to overcome the difficulties such as the much higher calculated viscosity in the outer region than that in the boundary regions, and the difficulty in continuously tracing moving wake centerlines encounted by other numerical methods. The agreement between the computational and experimental results is generally good. The sweeping characteristic of wakes, the influence of unsteadiness on incidence and the decaying features of unsteady velocities, pressure are included in the paper.

scholarly journals PEMAHAMAN METODE NUMERIK MENGGUNAKAN PEMPROGRMAN MATLAB (Studi Kasus : Metode Secant)

2017 ◽  
Vol 1 (1) ◽  
pp. 89
Author(s):  
Melda Panjaitan
Keyword(s):  
Approximate Solution ◽  
Problem Solving ◽  
Numerical Methods ◽  
Numerical Method ◽  
Mathematical Problem ◽  
Secant Method ◽  
Mathematical Problem Solving ◽  
Real Solution ◽  
True Solution ◽  
Solution Approach

Abstract - The numerical method is a powerful mathematical problem solving tool. With numerical methods, we get a solution that approaches or approaches a true solution so that a numerical solution is also called an approximate solution or solution approach, but almost the solution can be made as accurately as we want. The solution almost certainly isn't exactly the same as the real solution, so there is a difference between the two. This difference is called an error. the solution using numerical methods is always in the form of numbers. The secant method requires two initial estimates that must enclose the roots of the equation. Keywords - Numerical Method, Secant Method

scholarly journals The Bi-dimensional space of Korenblum and composition operator

2015 ◽  
Vol 62 (1) ◽  
pp. 1-12
Author(s):  
José A. Guerrero ◽  
Nelson Merentes ◽  
José L. Sánchez
Keyword(s):  
Banach Space ◽  
Composition Operator ◽  
Real Function ◽  
Dimensional Space ◽  
Similar Type ◽  
Functions Of Two Variables ◽  
Real Functions ◽  
Uniformly Continuous ◽  
Uniformly Bounded

Abstract In this paper we present the concept of total κ-variation in the sense of Hardy-Vitali-Korenblum for a real function defined in the rectangle Iab⊂R2. We show that the space κBV(Iab, R) of real functions of two variables with finite total κ-variation is a Banach space endowed with the norm ||f||κ = |f (a)| + κTV( f, Iab). Also, we characterize the Nemytskij composition operator H that maps the space of functions of two real variables of bounded κ-variation κBV(Iab, R) into another space of a similar type and is uniformly bounded (or Lipschitzian or uniformly continuous).

scholarly journals Semi-Precise Analytical Method for Investigating the Liftoff Variation on the Hall Sensor in Metal Defect Sensing

Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5539
Author(s):  
Ali Azad ◽  
Jong-Jae Lee ◽  
Namgyu Kim
Keyword(s):  
Numerical Methods ◽  
Hall Effect ◽  
Numerical Method ◽  
Surface Defects ◽  
Simulation Method ◽  
Hall Sensor ◽  
Induced Current ◽  
Element Analysis ◽  
Hall Effect Sensor ◽  
Conventional Numerical Method

Hall-effect sensors are used to detect metal surface defects both experimentally and numerically. The gap between the specimen and the sensor, called the liftoff, is assumed to remain constant, while a slight misplacement of a sample may lead to incorrect measurements by the Hall-effect sensor. This paper proposes a numerical simulation method to mitigate the liftoff issue. Owing to the complexity of conducting precise finite-element analysis, rather than obtaining the induced current in the Hall sensor, only the magnetic flux leakage is obtained. Thus, to achieve a better approximation, a numerical method capable of obtaining the induced current density in the circumferential direction in terms of the inspection direction is also proposed. Signals of the conventional and proposed approximate numerical methods affected by the sensor liftoff variation were obtained and compared. For small liftoffs, both conventional and proposed numerical methods could identify notch defects, while as the liftoff increased, no defect could be identified using the conventional numerical method. Furthermore, experiments were performed using a variety of liftoff configurations. Based on the results, considering the threshold of the conventional numerical method, defects were detected for greater liftoffs, but misdetection did not occur.

scholarly journals On some properties of the conformable fractional derivative

2020 ◽  
Vol 6 (2) ◽  
pp. 210-217
Author(s):  
Radouane Azennar ◽  
Driss Mentagui
Keyword(s):  
Fractional Derivative ◽  
Conformable Fractional Derivative ◽  
Intermediate Value Theorem ◽  
Definition Of ◽  
Intermediate Value

AbstractIn this paper, we prove that the intermediate value theorem remains true for the conformable fractional derivative and we prove some useful results using the definition of conformable fractional derivative given in R. Khalil, M. Al Horani, A. Yousef, M. Sababhehb [4].

Forty-Eight Ordinate Harmonic Analysis and the Harmonic Spectrum of Two-Cycle Diesel Torque

1940 ◽  
Vol 7 (4) ◽  
pp. A158-A160
Author(s):  
Nancy Klock
Keyword(s):  
Diesel Engine ◽  
Numerical Methods ◽  
Harmonic Analysis ◽  
Numerical Method ◽  
Gasoline Engine ◽  
Harmonic Spectrum ◽  
Torsional Vibrations ◽  
Harmonic Content ◽  
Good Account ◽  
Torque Curve

Abstract For the harmonic analysis of periodic curves, machines as well as numerical methods are available. The machines are expensive and not generally available, and time is required to learn their operation. Therefore, an occasional analysis of a curve consumes even less time by the numerical method than by the machine. The best known numerical method is that of Runge (1) described in many places; a good account is found in Scarborough’s book (2). The principle is clear, but writers usually give the method for 6, 12, or 24 ordinates for the sake of simplicity, which is not sufficiently accurate for most applications. In this paper the 48-ordinate scheme is fully given in Tables 1, 2, and 3. For the analysis of torsional vibrations the harmonic content of the torque curve of the disturbing engine is required. Such analyses have been published for the four-cycle Diesel engine (3) and for the four-cycle gasoline engine for aviation purposes (4). But to the author’s knowledge none have been published for the two-cycle Diesel engine. Such a spectrum is given herein.

scholarly journals Numerical simulation of minor losses coefficient on the example of elbows

2018 ◽  
Vol 180 ◽  
pp. 02093
Author(s):  
Smyk Emil ◽  
Mrozik Dariusz ◽  
Olszewski Łukasz ◽  
Peszyński Kazimierz
Keyword(s):  
Numerical Simulation ◽  
Numerical Methods ◽  
Numerical Method ◽  
Cross Section ◽  
Analytical Methods ◽  
Circular Cross Section ◽  
Experimental Methods ◽  
Loss Coefficient ◽  
Complicated Problem ◽  
Minor Losses

Determining of minor losses coefficient is very complicated problem. Analytical methods are often very difficult and experimental methods are very expensive and time-consuming. Consequently, the use of numerical methods seems to be a good solution, but there are no publications describing this issue. Therefore, the paper is describing the numerical method of determining the minor loss coefficient ξ on the example of elbows with circular cross-section.

scholarly journals A New Algorithm for Solving Terminal Value Problems of q-Difference Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Yong-Hong Fan ◽  
Lin-Lin Wang
Keyword(s):  
Exact Solution ◽  
Numerical Methods ◽  
Error Estimate ◽  
Numerical Solution ◽  
Numerical Method ◽  
Difference Equations ◽  
Initial Value Problems ◽  
Convergence Speed ◽  
Initial Value ◽  
Delta Derivatives

We propose a new algorithm for solving the terminal value problems on a q-difference equations. Through some transformations, the terminal value problems which contain the first- and second-order delta-derivatives have been changed into the corresponding initial value problems; then with the help of the methods developed by Liu and H. Jafari, the numerical solution has been obtained and the error estimate has also been considered for the terminal value problems. Some examples are given to illustrate the accuracy of the numerical methods we proposed. By comparing the exact solution with the numerical solution, we find that the convergence speed of this numerical method is very fast.

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