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 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 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.

scholarly journals HERONIAN MEAN DERIVATIVE-BASED SIMPSON’S-TYPE SCHEME FOR RIEMANN-STIELTJES INTEGRAL

2021 ◽  
Vol 16 (3) ◽  
Author(s):  
Kashif Memon
Keyword(s):  
Computational Cost ◽  
Stieltjes Integral ◽  
Basic Form ◽  
Order Of Accuracy ◽  
Riemann Integral ◽  
Cpu Time ◽  
Quadrature Scheme ◽  
Composite Form ◽  
Theoretical Results ◽  
Heronian Mean

In this paper, a new heronian mean derivative-based quadrature scheme of Simpson’s 1/3-type is proposed for the approximation of the Riemann-Stieltjes integral (RS-integral). Theorems are proved related to the basic form, composite form, local and global errors of the new scheme for the RS-integral. The reduction of the new proposed scheme is verified using g(t) = t for Riemann integral. The theoretical results of the new proposed scheme have been proved by experimental work using programming in MATLAB against existing schemes. The order of accuracy, computational cost and average CPU time (in seconds) of the new proposed scheme are determined. The results obtained show the effectiveness of the proposed scheme compared to the existing schemes.

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.

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.

Double integral involving G-function of two variables

2020 ◽  
pp. 333-338
Author(s):  
Shukla Vinay Kumar
Keyword(s):  
Integral Equation ◽  
Population Density ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Research Paper ◽  
Statistical Distribution ◽  
Double Integral ◽  
Expansion Formulae ◽  
Function Of Two Variables ◽  
Double Integrals

In the study of certain boundary value problems integrals are useful with their connections. To obtain expansion formulae it also helps. In the study of integral equation, probability and statistical distribution, integrals are also used. To measure population density within a certain area, we can also use integrals. With integrals we can analyzed anything that changes in time. The object of this research paper is to establish a double integrals involving G-Function of two variables.

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).

scholarly journals Weighted generalization of some inequalities for double integrals

2021 ◽  
Vol 110 (124) ◽  
pp. 71-79
Author(s):  
Mehmet Sarikaya ◽  
Hüseyin Budak
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Double Integral ◽  
Double Integrals

We give some weighted double integral inequalities of Hermite-Hadamard type for co-ordinated convex functions in a rectangle from R2. The inequalities obtained provide generalizations of some result given in earlier works.

scholarly journals Tauberian conditions under which convergence follows from Cesàro summability of double integrals over R2

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3425-3440
Author(s):  
Gökşen Fındık ◽  
İbrahim Çanak
Keyword(s):  
Continuous Function ◽  
The Other ◽  
Cesàro Summability ◽  
Double Integral ◽  
Tauberian Conditions ◽  
Summability Methods ◽  
Cesaro Summability ◽  
The Difference ◽  
Complex Valued ◽  
Double Integrals

For a real- or complex-valued continuous function f over R2+:= [0,1) x [0,1), we denote its integral over [0,u] x [0,v] by s(u,v) and its (C,1, 1) mean, the average of s(u,v) over [0,u] x [0,v], by ?(u,v). The other means (C,1,0) and (C; 0; 1) are defined analogously. We introduce the concepts of backward differences and the Kronecker identities in different senses for double integrals over R2+. We give onesided and two-sided Tauberian conditions based on the difference between double integral of s(u, v) and its means in different senses for Ces?ro summability methods of double integrals over [0,u] x [0,v] under which convergence of s(u,v) follows from integrability of s(u,v) in different senses.

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