scholarly journals Complete semi-analytical treatment of weakly singular integrals on planar triangles via the direct evaluation method

2010 ◽  
Vol 83 (12) ◽  
pp. 1625-1650 ◽  
Author(s):  
Athanasios G. Polimeridis ◽  
Juan R. Mosig
Keyword(s):  
Evaluation Method ◽  
Singular Integrals ◽  
Analytical Treatment ◽  
Direct Evaluation ◽  
Weakly Singular

A Singularity Cancellation Technique for Weakly Singular Integrals on Higher Order Surface Descriptions

2013 ◽  
Vol 61 (4) ◽  
pp. 2347-2352 ◽  
Author(s):  
N. V. Nair ◽  
A. J. Pray ◽  
J. Villa-Giron ◽  
B. Shanker ◽  
D. R. Wilton
Keyword(s):  
Singular Integrals ◽  
Higher Order ◽  
Weakly Singular ◽  
Order Surface

scholarly journals Rational Transformations for Evaluating Singular Integrals by the Gauss Quadrature Rule

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 677
Author(s):  
Beong In Yun
Keyword(s):  
Numerical Evaluation ◽  
Singular Integrals ◽  
Quadrature Rule ◽  
Transformation Method ◽  
Gauss Quadrature ◽  
Cauchy Principal ◽  
Weakly Singular ◽  
Principal Value ◽  
Transformation Methods ◽  
Gauss Quadrature Rule

In this work we introduce new rational transformations which are available for numerical evaluation of weakly singular integrals and Cauchy principal value integrals. The proposed rational transformations include parameters playing an important role in accelerating the accuracy of the Gauss quadrature rule used for the singular integrals. Results of some selected numerical examples show the efficiency of the proposed transformation method compared with some existing transformation methods.

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