scholarly journals On the application of two symmetric Gauss Legendre quadrature rules for composite numerical integration over a triangular surface

2007 ◽  
Vol 190 (1) ◽  
pp. 21-39 ◽  
Author(s):  
H.T. Rathod ◽  
K.V. Nagaraja ◽  
B. Venkatesudu
Keyword(s):  
Numerical Integration ◽  
Quadrature Rules ◽  
Legendre Quadrature

scholarly journals Application of MATLAB Symbolic Maths with Variable Precision Arithmetic (VPA) to Compute Some High Order Gauss Legendre Quadrature Rules

1970 ◽  
Vol 29 ◽  
pp. 117-125
Author(s):  
HT Rathod ◽  
RD Sathish ◽  
Md Shafiqul Islam ◽  
Arun Kumar Gali
Keyword(s):  
Gaussian Quadrature ◽  
High Order ◽  
Quadrature Rules ◽  
Zeros Of Polynomials ◽  
Matlab Program ◽  
Present Context ◽  
First Time ◽  
Legendre Quadrature ◽  
Weight Coefficients ◽  
Integration Rules

Gauss Legendre Quadrature rules are extremely accurate and they should be considered seriously when many integrals of similar nature are to be evaluated. This paper is concerned with the derivation and computation of numerical integration rules for the three integrals: (See text for formulae) which are dependent on the zeros and the squares of the zeros of Legendre Polynomial and is quite well known in the Gaussian Quadrature theory. We have developed the necessary MATLAB programs based on symbolic maths which can compute the sampling points and the weight coefficients and are reported here upto 32 – digits accuracy and we believe that they are reported to this accuracy for the first time. The MATLAB programs appended here are based on symbolic maths. They are very sophisticated and they can compute Quadrature rules of high order, whereas one of the recent MATLAB program appearing in reference [21] can compute Gauss Legendre Quadrature rules upto order twenty, because the zeros of Legendre polynomials cannot be computed to desired accuracy by MATLAB routine roots (……..). Whereas we have used the MATLAB routine solve (……..) to find zeros of polynomials which is very efficient. This is worth noting in the present context. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 29 (2009) 117-125  DOI: http://dx.doi.org/10.3329/ganit.v29i0.8521 

scholarly journals Midpoint Derivative-Based Closed Newton-Cotes Quadrature

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Weijing Zhao ◽  
Hongxing Li
Keyword(s):  
Numerical Integration ◽  
Computational Cost ◽  
Point Of View ◽  
Quadrature Rules ◽  
Numerical Examples ◽  
Error Terms

A novel family of numerical integration of closed Newton-Cotes quadrature rules is presented which uses the derivative value at the midpoint. It is proved that these kinds of quadrature rules obtain an increase of two orders of precision over the classical closed Newton-Cotes formula, and the error terms are given. The computational cost for these methods is analyzed from the numerical point of view, and it has shown that the proposed formulas are superior computationally to the same order closed Newton-Cotes formula when they reduce the error below the same level. Finally, some numerical examples show the numerical superiority of the proposed approach with respect to closed Newton-Cotes formulas.

scholarly journals Efficient Quadrature Rules for Numerical Integration Based on Linear Legendre Multi-Wavelets

2019 ◽  
Vol 1366 ◽  
pp. 012092
Author(s):  
Nur Neesha Alimin ◽  
Ahmad Fadly Nurullah Rasedee ◽  
Mohammad Hasan Abdul Sathar ◽  
Anvarjon A. Ahmedov ◽  
Muhammad Asyraf Asbullah
Keyword(s):  
Numerical Integration ◽  
Quadrature Rules
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