scholarly journals Calculation of Chakalov-Popoviciu quadratures of Radau and Lobatto type

2002 ◽  
Vol 43 (3) ◽  
pp. 429-447 ◽  
Author(s):  
Miodrag M. Spalević
Keyword(s):  
Numerical Method ◽  
Quadrature Formula ◽  
Spline Function ◽  
Finite Interval ◽  
Analytic Formula ◽  
Numerical Results ◽  
Quadrature Formulae

AbstractA numerical method for calculation of the generalized Chakalov-Popoviciu quadrature formulae of Radau and Lobatto type, using the results given for the generalized Chakalov-Popoviciu quadrature formula, is given. Numerical results are included. As an application we discuss the problem of approximating a function f on the finite interval I = [a, b] by a spline function of degree m and variable defects dv, with n (variable) knots, matching as many of the initial moments of f as possible. An analytic formula for the coefficients in the generalized Chakalov-Popoviciu quadrature formula is given.

scholarly journals Optimization of a k-covering of a bounded set with circles of two given radii

2021 ◽  
Vol 11 (1) ◽  
pp. 232-240
Author(s):  
Alexander V. Khorkov ◽  
Shamil I. Galiev
Keyword(s):  
Linear Programming ◽  
Numerical Method ◽  
Lower Bounds ◽  
Integer Linear Programming ◽  
Numerical Results ◽  
Programming Models ◽  
Bounded Set ◽  
The Given

Abstract A numerical method for investigating k-coverings of a convex bounded set with circles of two given radii is proposed. Cases with constraints on the distances between the covering circle centers are considered. An algorithm for finding an approximate number of such circles and the arrangement of their centers is described. For certain specific cases, approximate lower bounds of the density of the k-covering of the given domain are found. We use either 0–1 linear programming or general integer linear programming models. Numerical results demonstrating the effectiveness of the proposed methods are presented.

scholarly journals Experiments and numerical calculation to determine aerodynamic characteristics of flows around 3D wings

2014 ◽  
Vol 36 (2) ◽  
pp. 133-143 ◽  
Author(s):  
Nguyen Hong Son ◽  
Hoang Thi Bich Ngoc ◽  
Dinh Van Phong ◽  
Nguyen Manh Hung
Keyword(s):  
Numerical Calculation ◽  
Wind Tunnel ◽  
Pressure Distribution ◽  
Numerical Method ◽  
Aerodynamic Characteristics ◽  
Numerical Results ◽  
Computational Method ◽  
Wing Surface ◽  
Thickness Profile

The report presents method and results of experiments in wind tunnel to determine aerodynamic characteristics of 3D wings by measuring pressure distribution on the wing surfaces. Simultaneously, a numerical method by using sources and doublets distributed on panel elements of wing surface also is carried out to calculate flows around 3D wings. This computational method allows solving inviscid problems for wings with thickness profile. The experimental and numerical results are compared to each other to verify the built program that permits to extend the range of applications with the variation of wing profiles, wing planforms, and incidence angles.

Numerical Analysis of the Effect of Diffusion and Creep Flow on Cavity Growth

2007 ◽  
Author(s):  
Frederick W. Brust ◽  
Joonyoung Oh
Keyword(s):  
Growth Rate ◽  
Numerical Method ◽  
Cavity Growth ◽  
Volume Growth ◽  
Numerical Results ◽  
Shape Evolution ◽  
Cavity Volume ◽  
Cavity Shape ◽  
Cavity Growth Rate ◽  
Fully Coupled

In this paper, intergranular cavity growth in regimes, where both surface diffusion and deformation enhanced grain boundary diffusion are important, is studied. In order to continuously simulate the cavity shape evolution and cavity growth rate, a fully-coupled numerical method is proposed. Based on the fully-coupled numerical method, a gradual cavity shape change is predicted and this leads to an adverse effect on the cavity growth rates. As the portion of the cavity volume growth due to jacking and viscoplastic deformation in the total cavity volume growth increases, the initially spherical cavity evolves to V-shaped cavity. The numerical results are physically more realistic compared to results in the previous studies. The present numerical results suggest that the cavity shape evolution and cavity growth rate based on an assumed cavity shape, whether spherical or crack-like, cannot be used in this regime due to transitional coupled growth mechanisms.

scholarly journals A Comparison between Adomian Decomposition and Tau Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Necdet Bildik ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Tau Method ◽  
Adomian Decomposition

We present a comparison between Adomian decomposition method (ADM) and Tau method (TM) for the integro-differential equations with the initial or the boundary conditions. The problem is solved quickly, easily, and elegantly by ADM. The numerical results on the examples are shown to validate the proposed ADM as an effective numerical method to solve the integro-differential equations. The numerical results show that ADM method is very effective and convenient for solving differential equations than Tao method.

IMPLEMENTATIONS OF BOUNDARY–DOMAIN INTEGRO-DIFFERENTIAL EQUATION FOR DIRICHLET BVP WITH VARIABLE COEFFICIENT

2016 ◽  
Vol 78 (6-5) ◽  
Author(s):  
Nurul Akmal Mohamed ◽  
Nur Fadhilah Ibrahim ◽  
Mohd Rozni Md Yusof ◽  
Nurul Farihan Mohamed ◽  
Nurul Huda Mohamed
Keyword(s):  
Differential Equation ◽  
Quadrature Formula ◽  
Spectral Properties ◽  
Variable Coefficient ◽  
Logarithmic Singularity ◽  
Neumann Series ◽  
Numerical Results ◽  
Analytic Method ◽  
Elliptic Type ◽  
Integro Differential Equation

In this paper, we present the numerical results of the Boundary-Domain Integro-Differential Equation (BDIDE) associated to Dirichlet problem for an elliptic type Partial Differential Equation (PDE) with a variable coefficient. The numerical constructions are based on discretizing the boundary of the problem region by utilizing continuous linear iso-parametric elements while the domain of the problem region is meshed by using iso-parametric quadrilateral bilinear domain elements. We also use a semi-analytic method to handle the integration that exhibits logarithmic singularity instead of using Gauss-Laguare quadrature formula. The numerical results that employed the semi-analytic method give better accuracy as compared to those when we use Gauss-Laguerre quadrature formula. The system of equations that obtained by the discretized BDIDE is solved by an iterative method (Neumann series expansion) as well as a direct method (LU decomposition method). From our numerical experiments on all test domains, the relative errors of the solutions when applying semi-analytic method are smaller than when we use Gauss-Laguerre quadrature formula for the integration with logarithmic singularity. Unlike Dirichlet Boundary Integral Equation (BIE), the spectral properties of the Dirichlet BDIDE is not known. The Neumann iterations will converge to the solution if and only if the spectral radius of matrix operator is less than 1. In our numerical experiment on all the test domains, the Neumann series does converge. It gives some conclusions for the spectral properties of the Dirichlet BDIDE even though more experiments on the general Dirichlet problems need to be carried out.

Aeroelastic Analysis of Oscillatory Blowing Control of the Airfoil’s Flutter at Large Attack Angle

2002 ◽  
Author(s):  
Jin Yan ◽  
Yuan Xin
Keyword(s):  
Numerical Method ◽  
Flow Separation ◽  
Lift Coefficient ◽  
High Accuracy ◽  
Numerical Results ◽  
Attack Angle ◽  
Fluid Structure ◽  
Aeroelastic Analysis

It is known that oscillatory blowing on the back of an airfoil can delay the flow separation and the stall. The purpose of the present paper is to apply the oscillatory blowing technique to the control of the airfoil’s flutter. High accuracy, high solution fluid-structure coupling numerical method is used in the study. The numerical results show that the steady blowing will weaken the flutter, but at the same time the excess blowing will make the lift coefficient to drop. The best blowing velocity can be found by the present numerical method. The influence of the frequency and the amplitude of the oscillatory blowing on the airfoil’s vibration is studied in the paper. The numerical results show that the oscillatory blowing is more efficient in the cases of flutter than steady blowing.

scholarly journals Solving Dual Fuzzy Nonlinear Equations via Shamanskii Method

2018 ◽  
Vol 7 (3.28) ◽  
pp. 89 ◽  
Author(s):  
Ibrahim Mohammed Sulaiman ◽  
Mustafa Mamat ◽  
Nurnadiah Zamri ◽  
Puspa Liza Ghazali
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Computational Cost ◽  
Numerical Results ◽  
Parametric Form ◽  
Solution Point ◽  
New Ideas

New ideas on numerical methods for solving fuzzy nonlinear equations have spread quickly across the globe. However, most of the methods available are based on Newton’s approach whose performance is impaired by either discontinuity or singularity of the Jacobian at the solution point. Also, the study of dual fuzzy nonlinear equations is yet to be explored by many researchers. Thus, in this paper, a numerical method to investigate the solution of dual fuzzy nonlinear equations is proposed. This method reduces the computational cost of Jacobian evaluation at every iteration. The fuzzy coefficients are presented in its parametric form. Numerical results obtained have shown that the proposed method is efficient. 

scholarly journals A Stable Recursive Algorithm for Evaluation of Ultimate Ruin Probabilities

1984 ◽  
Vol 14 (1) ◽  
pp. 53-59 ◽  
Author(s):  
Marc Goovaerts ◽  
Florian de Vylder
Keyword(s):  
Recursive Algorithm ◽  
Numerical Results ◽  
Integrodifferential Equations ◽  
Ruin Probabilities ◽  
Tolerance Level ◽  
Quadrature Formulae

AbstractProbabilities of ruin are solutions of differential or integrodifferential equations. Solving such equations numerically can be performed by means of approximate quadrature formulae for the convolution part of the equation. In this contribution it is shown how applicable recursion formulae, giving results within a prescribed tolerance level, can be obtained. Some numerical results are displayed.

Stochastic Analysis to Truss Spar Platform in Deep Sea

2013 ◽  
Vol 477-478 ◽  
pp. 809-812
Author(s):  
Yan Wang ◽  
Rui Gao ◽  
Ling Qiang Yang
Keyword(s):  
Numerical Method ◽  
Deep Sea ◽  
Stochastic Analysis ◽  
Numerical Results ◽  
Model Parameters ◽  
Regular Waves ◽  
Spar Platform ◽  
Truss Spar Platform ◽  
Wave Basin ◽  
Truss Spar

Truss spar model was tested using regular waves in a wave basin and the responses in surge, heave and pitch were measured. A program was developed to determine the responses using numerical method. This program was run using the model parameters. The results are agreed well with the corresponding results obtained from the test measurements. Then this program was applied to a prototype spar simulated results were compared with the corresponding numerical results and test measurements.

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