Numerical integration of analytic functions

2012 ◽  
Author(s):  
Gradimir V. Milovanović ◽  
Dobrilo e Tošić ◽  
Miloljub Albijanić
Keyword(s):  
Numerical Integration ◽  
Analytic Functions

scholarly journals A quadrature rule of Lobatto-Gaussian for numerical integration of analytic functions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Sanjit Kumar Mohanty ◽  
Rajani Ballav Dash
Keyword(s):  
Theoretical Prediction ◽  
Numerical Integration ◽  
Error Estimation ◽  
Analytic Functions ◽  
Quadrature Rule ◽  
Asymptotic Error

<p style='text-indent:20px;'>A novel quadrature rule is formed combining Lobatto six point transformed rule and Gauss-Legendre five point transformed rule each having precision nine. The mixed rule so formed is of precision eleven. Through asymptotic error estimation the novelty of the quadrature rule is justified. Some test integrals have been evaluated using the mixed rule and its constituents both in non-adaptive and adaptive modes. The results are found to be quite encouraging for the mixed rule which is in conformation with the theoretical prediction.</p>

Numerical Integration of Non-analytic Functions

1964 ◽  
Vol 43 (1-4) ◽  
pp. 45-50 ◽  
Author(s):  
P C Waterman ◽  
J. M. Yos ◽  
R J. Abodeely
Keyword(s):  
Numerical Integration ◽  
Analytic Functions

scholarly journals A generalized Birkhoff–Young quadrature formula

2016 ◽  
Vol 32 (2) ◽  
pp. 203-213
Author(s):  
GRADIMIR V. MILOVANOVIC ◽  
◽  
MILOLJUB ALBIJANIC ◽  
Keyword(s):  
Numerical Integration ◽  
Explicit Form ◽  
Quadrature Formula ◽  
Analytic Functions ◽  
Maximal Degree ◽  
Special Cases

A generalized (4n + 1)-point Birkhoff–Young quadrature of interpolatory type with the maximal degree of precision for numerical integration of analytic functions is derived. An explicit form of the node polynomial of such kind of quadratures is obtained. Special cases and an example are presented.

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