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Cauchy Principal Value Contour Integral with Applications [PDF]
Entropy, 2017 Cauchy principal value is a standard method applied in mathematical applications by which an improper, and possibly divergent, integral is measured in a balanced way around singularities or at infinity.
Matilde Legua, Luis M. Sánchez-Ruiz
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Numerical evaluation of a generalized Cauchy principal value [PDF]
Miskolc Mathematical Notes, 2000 Summary: A method is presented for the evaluation of a generalized Cauchy principal value of an improper integral. The integral is transformed into a Riemann integral which is evaluated using Romberg integration. This method is very convenient for computational purposes.
Nyíri, András, Baranyi, László
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Spline approximation for Cauchy principal value integrals [PDF]
Journal of Computational and Applied Mathematics, 1990 The author considers the problem of numerical evaluation of Cauchy principal value integrals of the form \(I(f^{(k)};y)=\oint^{b}_{a}w(x)f^{(k)}(x)/(x-y)dx\quad (k=0,1,...).\) She examines quadrature rules of the form: \(I(f^{(k)};y)\approx I_ n(f^{(k)};y)=\sum^{n}_{i=0}w_ i^{(k)}(y)f(x_ i),\) where \(a=x_ ...
Palamara Orsi, Annamaria
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On the Evaluation of Oscillatory Kind with Cauchy Principal Value
Journal of Applied Mathematics and Physics, 2021 In this paper, we discuss the integrals of oscillatory kind function with Cauchy principal value in point zero which have the form like , where f (x) is smooth function and r is odd integer. In this integral, xr has several stationary points , and the Cauchy principal value . We use some integral technique to transform it into the form like so that we
Changhao Li
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A Class of Quadrature Rules for Complex Cauchy Principal Value Integrals [PDF]
International Journal of Mathematical, Engineering and Management Sciences, 2023 This article is fully devoted to the numerical approximation of Cauchy-type integrals in the complex plane. A class of degree eight quadrature rules is formulated from a family of Gauss-type two-point rules based on the method of extrapolation. The basic
Arup Kumar Saha +2 more
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Extended Error Expansion of Classical Midpoint Rectangle Rule for Cauchy Principal Value Integrals on an Interval [PDF]
Journal of Mathematics, 2021 The classical composite midpoint rectangle rule for computing Cauchy principal value integrals on an interval is studied. By using a piecewise constant interpolant to approximate the density function, an extended error expansion and its corresponding ...
Chunxiao Yu, Lingling Wei
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Fault Detection Approach of Cyclotron Ion Sources Based on KPCA-ISSA-SVM [PDF]
SensorsTo address the challenges of difficult feature extraction and suboptimal parameter configuration for cyclotron ion source fault diagnosis in complex environments, this study proposes an intelligent diagnostic framework integrating Kernel Principal ...
Yunlong Li +6 more
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An automatic quadrature for Cauchy principal value integrals [PDF]
Mathematics of Computation, 1991 An automatic quadrature is presented for computing Cauchy principal value integrals Q ( f ; c
Takemitsu Hasegawa, Tatsuo Torii
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Surveys in Mathematics and its Applications, 2021 The Hilbert transform is essentially the only singular operator in one dimension. This undoubtedly make it one of the most important linear operator in harmonic analysis.
Edisson Arley Arcos +1 more
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Radial basis functions for solving the singular boundary integral equation of the compressible fluid flow around obstacles [PDF]
ITM Web of Conferences, 2020 In this paper we find a numerical solution for the Singular Boundary Integral Equation (SBIE), with sources distribution, of the compressible fluid flow around obstacles.
Grecu Luminiţa
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