Cauchy-type integrals and integral equations with logarithmic singularities

DOI10.1007/BF00042797zbMath0394.65049OpenAlexW2003646628MaRDI QIDQ1252711

A. C. Chrysakis, Nikolaos I. Ioakimidis, Pericles S. Theocaris

Publication date: 1979

Published in: Journal of Engineering Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00042797

zbMATH Keywords

Numerical ExampleCauchy-Type Integral EquationsCauchy-Type IntegralsCrack Problem of Plane ElasticityGauss-Type Quadrature MethodsLogarithmic Singularities

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Numerical methods for integral equations (65R20) Numerical quadrature and cubature formulas (65D32) Integral equations with kernels of Cauchy type (45E05)

Related Items (7)

On the validity of the singular integral equations of elasticity problems at points of loading discontinuities ⋮ The general type of finite-part singular integrals and integral equations with logarithmic singularities used in fracture mechanics ⋮ Discrete collocation method for Volterra type weakly singular integral equations with logarithmic kernels ⋮ Application of the method of singular integral equations to elasticity problems with concentrated loads ⋮ Finite-dimensional approximations of singular integrals and direct methods of solution of singular integral and integrodifferential equations ⋮ The V-notched elastic half-plane problem ⋮ Numerical solution of Cauchy type singular integral equations with logarithmic weight, based on arbitrary collocation points

Cites Work

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• Some Gauss-type formulae for the evaluation of Cauchy principal values of integrals
• [https://portal.mardi4nfdi.de/wiki/Publication:3214283 Numerical Construction of Gaussian Quadrature Formulas for � � 1 0   (-Log x)⋅x α ⋅f(x) ⋅dx     and     � � ∞ 0 E m (x) ⋅f(x) ⋅dx]
• On the Evaluation of Some Integrals Occurring in Scattering Problems
• ORTHOGONAL POLYNOMIAL SOLUTIONS TO SOME MIXED BOUNDARY-VALUE PROBLEMS IN ELASTICITY THEORY
• Modified gauss-jacobi quadrature formulas for the numerical evaluation of cauchy type singular integrals
• A Unified Approach to Quadrature Rules with Asymptotic Estimates of Their Remainders

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