On the numerical evaluation of derivatives of Cauchy principal value integrals
Copyright policy )On the numerical evaluation of derivatives of Cauchy principal value integrals
Quadrature rules for the approximate evaluation of derivatives of Cauchy principal value integrals (with respect to the free variable inside the integral) can be obtained by formal differentiations of the right sides of the corresponding quadrature rules (without derivatives). The justification of this method, under appropriate conditions, is presented in this short communication. The results of this short communication are also applicable to the numerical evaluation of a class of finite-part integrals and to the numerical solution of singular integrodifferential equations.
- University of Patras Greece
differentiation under the integral sign, Cauchy type integrals, convergence, principal value integrals, Gaussian quadrature rules, finite-part integrals, Taylor's formula, Numerical quadrature and cubature formulas, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, Approximate quadratures
differentiation under the integral sign, Cauchy type integrals, convergence, principal value integrals, Gaussian quadrature rules, finite-part integrals, Taylor's formula, Numerical quadrature and cubature formulas, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, Approximate quadratures
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