An efficient transformation with Gauss quadrature rule for weakly singular integrals

2001 ◽  
Vol 17 (12) ◽  
pp. 881-891 ◽  
Author(s):  
Beong In Yun
Keyword(s):  
Singular Integrals ◽  
Quadrature Rule ◽  
Gauss Quadrature ◽  
Efficient Transformation ◽  
Weakly Singular ◽  
Gauss Quadrature Rule

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.

scholarly journals A New Application of Gauss Quadrature Method for Solving Systems of Nonlinear Equations

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 432
Author(s):  
Hari M. Srivastava ◽  
Javed Iqbal ◽  
Muhammad Arif ◽  
Alamgir Khan ◽  
Yusif S. Gasimov ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Nonlinear Boundary ◽  
Quadrature Rule ◽  
Gauss Quadrature ◽  
New Method ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Numerical Comparison ◽  
Nonlinear Boundary Value Problems ◽  
Gauss Quadrature Rule

In this paper, we introduce a new three-step Newton method for solving a system of nonlinear equations. This new method based on Gauss quadrature rule has sixth order of convergence (with n=3). The proposed method solves nonlinear boundary-value problems and integral equations in few iterations with good accuracy. Numerical comparison shows that the new method is remarkably effective for solving systems of nonlinear equations.

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