• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권4호
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• pp.347-355
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• 2023

For numerical evaluation of Cauchy principal value integrals, we present a simple rational function with a parameter satisfying some reasonable conditions. The proposed rational function is employed in coordinate transformation for accelerating the accuracy of the Gauss quadrature rule. The efficiency of the proposed rational transformation method is demonstrated by the numerical result of a selected test example.

• 대한수학회지
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• 제48권1호
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• pp.133-146
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• 2011

We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations compared with those of existing non-linear transformation methods.

• 대한수학회보
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• 제39권4호
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• pp.543-559
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• 2002

Some inequalities and approximations for the finite filbert transform by the use of Ostrowski type inequalities for absolutely continuous functions are given.