scholarly journals Asymptotic expressions for the remainder term in the quadrature formula of Gauss-Jacobi type

2012 ◽  
Vol 21 (1) ◽  
pp. 1-11
Author(s):  
ANA MARIA ACU ◽  
◽  
DANIEL FLORIN SOFONEA ◽  
Keyword(s):  
Error Analysis ◽  
Quadrature Formula ◽  
Positive Operator ◽  
Remainder Term ◽  
Linear Positive Operator ◽  
Asymptotic Expressions

In this paper we have considered error analysis for a quadrature formula which is obtained by integration of linear positive operator. The asymptotic expressions for remainder term of Gauss-Jacobi type quadrature formula are also given.

scholarly journals The Bernstein quadrature formula revised

2014 ◽  
Vol 30 (3) ◽  
pp. 275-282
Author(s):  
DAN BARBOSU ◽  
◽  
GHEORGHE ARDELEAN ◽  
Keyword(s):  
Quadrature Formula ◽  
Remainder Term ◽  
Approximation Formula ◽  
Numerical Examples ◽  
Bernstein Approximation

Starting with the Bernstein approximation formula on the interval [a, b] a corresponding composite quadrature formula is constructed. Its coefficients and an estimation for the remainder term are determined. Numerical examples are also presented.

scholarly journals ON THE TRAPEZOID QUADRATURE FORMULA FOR LIPSCHITZIAN MAPPINGS AND APPLICATIONS

1999 ◽  
Vol 30 (2) ◽  
pp. 133-138
Author(s):  
SEVER SILVESTRU DRAGOMIR
Keyword(s):  
Quadrature Formula ◽  
Remainder Term ◽  
Lipschitzian Mappings ◽  
Special Means

The estimation of the remainder term in trapezoid formula for lipschitzian mappings are given. Applications for special means are also pointed out.

Higher order two-scale finite element error analysis for thermoelastic problem in quasi-periodic perforated structure

2017 ◽  
Vol 28 (07) ◽  
pp. 1750097
Author(s):  
Mingxiang Deng ◽  
Yongping Feng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Analysis ◽  
Thermal Behavior ◽  
Higher Order ◽  
Numerical Results ◽  
Thermoelastic Problem ◽  
Asymptotic Expressions ◽  
Element Error ◽  
Element Method

In this paper, one new coupled higher order two-scale finite element method (TSFEM) for thermoelastic problem in composites is proposed. Firstly, some new two-scale asymptotic expressions and homogenization formulations for the problem are briefly given. Next, some high–low coupled approximate errors corresponding to TSFEM are analyzed. Finally, some numerical results of the displacement and the increment of temperature are presented, which show that TSFEM is an effective method for predicting the mechanical and the thermal behavior of composites in quasi-periodic perforated structure.

scholarly journals Error bounds for Gauss-Lobatto quadrature formula with multiple end points with Chebyshev weight function of the third and the fourth kind

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 231-239 ◽  
Author(s):  
Ljubica Mihic ◽  
Aleksandar Pejcev ◽  
Miodrag Spalevic
Keyword(s):  
Weight Function ◽  
Quadrature Formula ◽  
Error Bounds ◽  
Analytic Functions ◽  
Remainder Term ◽  
Applied Mathematics ◽  
Maximum Modulus ◽  
End Points ◽  
The Third ◽  
Fourth Kind

For analytic functions the remainder terms of quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points -+1, for Gauss-Lobatto quadrature formula with multiple end points with Chebyshev weight function of the third and the fourth kind. Starting from the explicit expression of the corresponding kernel, derived by Gautschi and Li, we determine the locations on the ellipses where maximum modulus of the kernel is attained. The obtained values confirm the corresponding conjectured values given by Gautschi and Li in paper [The remainder term for analytic functions of Gauss-Radau and Gauss-Lobatto quadrature rules with multiple end points, Journal of Computational and Applied Mathematics 33 (1990) 315-329.]

scholarly journals The remainder term of Gauss-Radau quadrature rule with single and double end point

2017 ◽  
Vol 102 (116) ◽  
pp. 73-83
Author(s):  
Ljubica Mihic
Keyword(s):  
Weight Function ◽  
Explicit Expression ◽  
Quadrature Formula ◽  
Remainder Term ◽  
Maximum Modulus ◽  
Quadrature Rule ◽  
Contour Integral ◽  
End Point

The remainder term of quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours for Gauss?Radau quadrature formula with the Chebyshev weight function of the second kind with double and single end point. Starting from the explicit expression of the corresponding kernel, derived by Gautschi and Li, we determine the locations on the ellipses where the maximum modulus of the kernel is attained.

scholarly journals Some applications of Shisha-Mond theorem

2014 ◽  
Vol 23 (2) ◽  
pp. 141-146
Author(s):  
DAN BARBOSU ◽  
Keyword(s):  
Positive Operator ◽  
Approximation Order ◽  
Linear Positive Operator

A result due to Shisha, O. and Mond, B., is recalled and some applications in the evaluation of approximation order by linear positive operator are presented.

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