scholarly journals A NEW AND EFFICIENT CENTROIDAL MEAN DERIVATIVE-BASED TRAPEZOIDAL SCHEME FOR NUMERICAL CUBATURE

2021 ◽  
Vol 16 (3) ◽  
Author(s):  
Kamran Malik
Keyword(s):  
Performance Evaluation ◽  
Numerical Experiments ◽  
Finite Range ◽  
Order Of Accuracy ◽  
Accurate Evaluation ◽  
Error Distributions ◽  
Composite Form ◽  
Error Terms ◽  
Proposed Modification ◽  
Double Integrals

This research presents a new and efficient Centroidal mean derivative-based numerical cubature scheme which has been proposed for the accurate evaluation of double integrals under finite range. The proposed modification is based on the Trapezoidal-type quadrature and cubature rules. The approximate values can only be obtained for some important applications to evaluate the complex double integrals. Higher precision and order of accuracy could be achieved by the proposed scheme. The schemes, in basic and composite forms, with local and global error terms are presented with necessary supporting arguments with their performance evaluation against conventional Trapezoid rule through some numerical experiments. The simultaneously observed error distributions of the proposed schemes are found to be lower than the conventional Trapezoidal cubature scheme in composite form

scholarly journals AN EFFICIENT TRAPEZOIDAL SCHEME FOR NUMERICAL CUBATURE WITH HERONIAN MEAN DERIVATIVE

2021 ◽  
Vol 16 (3) ◽  
Author(s):  
Kamran Malik
Keyword(s):  
Performance Evaluation ◽  
Numerical Experiments ◽  
Double Integral ◽  
Order Of Accuracy ◽  
Error Distributions ◽  
Integral Scheme ◽  
Composite Form ◽  
Error Terms ◽  
Double Integrals ◽  
Heronian Mean

This study focuses on the Heronian mean derivative-based numerical cubature scheme to better evaluate double integrals’ infinite limits. The proposed modifications rely on the Trapezoidal-type quadrature and cubature schemes. The aforementioned proposed scheme is important to numerically evaluate the complex double integrals, where the exact value is not available but the approximate values can only be obtained. With regards to higher precision and order of accuracy, the proposed Heronian derivative-based double integral scheme provides efficient results. The discussed scheme, in basic and composite forms, with local and global error terms is presented with necessary proofs with their performance evaluation against conventional Trapezoid rule through some numerical experiments. The consequently observed error distributions of the aforementioned scheme are found to be lower than the conventional Trapezoidal cubature scheme in composite form

scholarly journals A PERFORMANCE EVALUATION OF TRAPEZOIDAL VARIANTS FOR NUMERICAL CUBATURE

2021 ◽  
Vol 16 (4) ◽  
Author(s):  
Kamran Malik
Keyword(s):  
Performance Evaluation ◽  
Numerical Experiments ◽  
Recent Literature ◽  
Local Error ◽  
Double Integral ◽  
Order Of Accuracy ◽  
Computational Costs ◽  
Derivative Free ◽  
Integral Scheme ◽  
Error Terms

In this work, double integration cubature schemes of Trapezoid type have been focused. Recently, some derivative-based Trapezoid-type schemes have been proposed in literature incorporating derivatives at means of the limits of integration. We carry out the exhaustive performance evaluation of the existing closed Newton-Cotes Trapezoidal (CNCT) double integral scheme with its derivative-based variants in recent literature. The derivative-free and derivative-based rules are discussed in basic forms with local error terms and composite forms with global error terms. The performance of the rules on some double integrals in the form of observed order of accuracy, computational costs and error drops demonstrates the encouraging performance of the derivative-based trapezoidal variants over the derivative-free scheme performing numerical experiments.

Development of a Driving Cycle for Amman City With Performance Evaluation for ICE Vehicle

2014 ◽  
Author(s):  
M. Abu Mallouh ◽  
B. W. Surgenor ◽  
E. Abdelhafez ◽  
M. Salah ◽  
M. Hamdan
Keyword(s):  
Performance Evaluation ◽  
Fuel Cell ◽  
Fuel Economy ◽  
Performance Comparison ◽  
Driving Cycle ◽  
Accurate Estimation ◽  
Accurate Evaluation ◽  
Driving Cycles ◽  
Considerable Research ◽  
Future Work

A good driving cycle is needed for accurate evaluation of a vehicle’s performance in terms of emission and fuel consumption. Driving cycles obtained for certain cities or countries are not usually applicable to other cities or countries. Therefore, considerable research has been conducted on developing driving cycles for certain cities and regions. In this paper, a driving cycle for a taxi in Amman city, the capital of Jordan, is developed. Significant differences are noted when comparing the Amman driving cycle with other driving cycles. A model of a gasoline powered vehicle is used to conduct a performance comparison in terms of fuel economy and emissions utilizing the developed Amman driving cycle and six other worldwide driving cycles. The developed Amman driving cycle is very useful in obtaining accurate estimation of fuel economy and emissions for vehicles running on Amman roads and will be used in future work to study the performance of hybrid fuel cell/ battery vehicles.

scholarly journals Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system

2020 ◽  
Vol 25 (6) ◽  
pp. 997-1014
Author(s):  
Ozgur Yildirim ◽  
Meltem Uzun
Keyword(s):  
Difference Scheme ◽  
Numerical Method ◽  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Finite Difference Schemes ◽  
Order Of Accuracy ◽  
Unconditionally Stable ◽  
First Order ◽  
The Difference ◽  
Weak Solvability

In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability.We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method.

scholarly journals Highway Performance Evaluation Index in Semiarid Climate Region Based on Fuzzy Mathematics

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Sanqiang Yang ◽  
Meng Guo ◽  
Xinlei Liu ◽  
Pidong Wang ◽  
Qian Li ◽  
...  
Keyword(s):  
Performance Evaluation ◽  
Pavement Design ◽  
Pavement Performance ◽  
Fuzzy Mathematics ◽  
Accurate Evaluation ◽  
Multi Index ◽  
Climate Region ◽  
Design Scheme ◽  
Semiarid Climate ◽  
Highway Pavement

Accurate evaluation and analysis of expressway pavement performance is a prerequisite for determining the pavement design scheme and maintenance scheme. Due to the fuzziness and randomness of many factors affecting the pavement performance, this paper relies on the reconstruction and expansion project of Xinglin section of the Taihang mountain expressway, a method of highway pavement performance evaluation based on fuzzy mathematics is proposed. The results show the following: ① the study uses the factor domain, the comment level domain, the fuzzy relationship matrix, the evaluation factor full vector, and the fuzzy comprehensive evaluation result vector five-step method. The method can be effectively combined with the multi-index comprehensive detection index used in the specification. ② Based on the multi-index comprehensive test and evaluation adopted in the specification, the performance grade of the old road surface was quantitatively evaluated by the iterative calculation of fuzzy mathematics that broke through the evaluation mode which was based on the traditional detection methods. The research results provide innovative theoretical methods for the accurate evaluation and analysis of highway pavement performance in the semiarid climate region and also play a technical supporting role for the pavement design scheme and maintenance scheme decision-making in the semiarid climate region.

FINITE-DIFFERENCE METHOD OF ORDER SIX FOR THE TWO-DIMENSIONAL STEADY AND UNSTEADY BOUNDARY-LAYER EQUATIONS

2005 ◽  
Vol 16 (05) ◽  
pp. 757-780 ◽  
Author(s):  
A. A. SALAMA ◽  
A. A. MANSOUR
Keyword(s):  
Boundary Layer ◽  
Numerical Experiments ◽  
Two Dimensional ◽  
Unsteady Boundary Layer ◽  
Order Of Accuracy ◽  
Unconditionally Stable ◽  
High Order Method ◽  
Boundary Layer Equations ◽  
Special Cases ◽  
Blasius Equation

In this article, we propose a high order method for solving steady and unsteady two-dimensional laminar boundary-layer equations. This method is convergent of sixth-order of accuracy. It is shown that this method is unconditionally stable. The unsteady separated stagnation point flow, the Falkner–Skan equation and Blasius equation are considered as special cases of these equations. Numerical experiments are given to illustrate our method and its convergence.

scholarly journals A NEW AND EFFICIENT SIMPSON’S 1/3-TYPE QUADRATURE RULE FOR RIEMANN-STIELTJES INTEGRAL

2020 ◽  
Vol 15 (11) ◽  
Author(s):  
Kashif Memon
Keyword(s):  
Computational Cost ◽  
Quadrature Rule ◽  
Test Problems ◽  
Stieltjes Integral ◽  
Rapid Convergence ◽  
Order Of Accuracy ◽  
Quadrature Scheme ◽  
Derivative Free ◽  
Composite Form ◽  
Successful Reduction

In this research paper, a new derivative-free Simpson 1/3-type quadrature scheme has been proposed for the approximation of the Riemann-Stieltjes integral (RSI). The composite form of the proposed scheme on the RSI has been derived using the concept of precision. The theorems concerning basic form, composite form, local and global errors of the new scheme have been proved theoretically. For the trivial case of the integrator in the proposed RS scheme, successful reduction to the corresponding Riemann scheme is proved. The performance of the proposed scheme has been tested by numerical experiments using MATLAB on some test problems of RS integrals from literature against some existing schemes. The computational cost, the order of accuracy and average CPU times (in seconds) of the discussed rules have been computed to demonstrate cost-effectiveness, time-efficiency and rapid convergence of the proposed scheme under similar conditions.

Analysis of Geometrically Consistent Schemes with Finite Range Interaction

2017 ◽  
Vol 22 (5) ◽  
pp. 1333-1361
Author(s):  
Hongliang Li ◽  
Pingbing Ming
Keyword(s):  
Error Estimate ◽  
Numerical Experiments ◽  
Optimal Error Estimate ◽  
Finite Range ◽  
Dimensional Problem ◽  
Optimal Error ◽  
Range Interaction ◽  
One Dimensional ◽  
Sharp Stability ◽  
Theoretical Results

AbstractWe analyze the geometrically consistent schemes proposed by E. Lu and Yang [6] for one-dimensional problem with finite range interaction. The existence of the reconstruction coefficients is proved, and optimal error estimate is derived under sharp stability condition. Numerical experiments are performed to confirm the theoretical results.

scholarly journals Towards Consensus Gene Ages

2016 ◽  
Author(s):  
Benjamin J. Liebeskind ◽  
Claire D. McWhite ◽  
Edward M. Marcotte
Keyword(s):  
Point Estimate ◽  
Consensus Algorithms ◽  
Inference Algorithms ◽  
Error Distributions ◽  
Error Terms ◽  
Or Gene ◽  
Different Sources ◽  
Per Gene ◽  
Gene Age ◽  
Substantial Uncertainty

Correctly estimating the age of a gene or gene family is important for a variety of fields, including molecular evolution, comparative genomics, and phylogenetics, and increasingly for systems biology and disease genetics. However, most studies use only a point estimate of a gene's age, neglecting the substantial uncertainty involved in this estimation. Here, we characterize this uncertainty by investigating the effect of algorithm choice on gene-age inference and calculate consensus gene ages with attendant error distributions for a variety of model eukaryotes. We use thirteen orthology inference algorithms to create gene-age datasets and then characterize the error around each age-call on a per-gene and per-algorithm basis. Systematic error was found to be a large factor in estimating gene age, suggesting that simple consensus algorithms are not enough to give a reliable point estimate. We also found that different sources of error can affect downstream analyses, such as gene ontology enrichment. Our consensus gene-age datasets, with associated error terms, are made fully available at so that researchers can propagate this uncertainty through their analyses (https://github.com/marcottelab/Gene-Ages).

A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems

2021 ◽  
pp. 1-63
Author(s):  
Marta D’Elia ◽  
Max Gunzburger ◽  
Christian Vollmann
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Discrete Systems ◽  
Sufficient Accuracy ◽  
Quadrature Rules ◽  
Finite Range ◽  
Nonlocal Problems ◽  
Nonlocal Models ◽  
Stiffness Matrices ◽  
Double Integrals

The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak forms involving double integrals which lead to discrete systems having higher assembly and solving costs due to possibly much lower sparsity compared to that of FEMs for PDEs. In addition, one may encounter nonsmooth integrands. In many nonlocal models, nonlocal interactions are limited to bounded neighborhoods that are ubiquitously chosen to be Euclidean balls, resulting in the challenge of dealing with intersections of such balls with the finite elements. We focus on developing recipes for the efficient assembly of FEM stiffness matrices and on the choice of quadrature rules for the double integrals that contribute to the assembly efficiency and also posses sufficient accuracy. A major feature of our recipes is the use of approximate balls, e.g. several polygonal approximations of Euclidean balls, that, among other advantages, mitigate the challenge of dealing with ball-element intersections. We provide numerical illustrations of the relative accuracy and efficiency of the several approaches we develop.

Sign in / Sign up

Export Citation Format

Share Document