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Modified Gauss rules for approximate calculation of some strongly singular integrals
Institution:Dep. Applied Mathematics I, Universidade de Vigo, Vigo, Spain;Dep. Innovacións Mariñas, Universidade da Coruña, A Coruña, Spain;Institute of Mathematics and Cybernetics, University of Economics ul. Komandorska 118/120, 53–345 Wroc?aw, Poland;Hausdorff Centre for Mathematics, University of Bonn, Germany;Mathematics Department, Istanbul University, Istanbul, Turkey;Department of Mathematics, University of Toronto, Toronto, Canada;Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary;Departamento de Métodos Estadísticos, Universidad de Zaragoza, Zaragoza, Spain;Departamento de Métodos Estadísticos, Universidad de Zaragoza, Zaragoza, Spain;Department of Mathematics, University of Denver, Denver, USA;Department of Mathematics, University of Toronto, Toronto, Canada
Abstract:The approach we follow consists in transforming the numerical evaluation of hyper-singular integrals into the calculation of a nearly singular integral whose mass is distributed according to a positive parameter ε. To evaluate the latter we apply a Gauss quadrature formula associated with a nearly singular weight function. It is estimated the error in terms of ε. Some numerical results are presented.
Keywords:Strongly singular integral  Cauchy principal value  Gauss quadrature formula
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