A method for the numerical solution of singular integral equations with a principal value integral

DOI10.1016/0020-7225(81)90148-8zbMath0476.73065OpenAlexW1985371499MaRDI QIDQ1160016

R. P. Srivastav, Apostolos Gerasoulis

Publication date: 1981

Published in: International Journal of Engineering Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0020-7225(81)90148-8

zbMATH Keywords

reduced to system of linear algebraic equationscompared with procedures based on Gauss-Chebyshev and Lobatto-Chebyshev quadrature formulaeexplicitly built into solution using index theoremintegral equation replaced by integral relations at discrete set of pointsintegrand approximated by piecewise linear functionsintegration in closed formsingular behavior of unknown function

Mathematics Subject Classification ID

Numerical quadrature and cubature formulas (65D32) Brittle damage (74R05) Theoretical approximation of solutions to integral equations (45L05) Integral equations with kernels of Cauchy type (45E05)

Related Items

Cubic Splines and Approximate Solution of Singular Integral Equations ⋮ Recent developments in the numerical solution of singular integral equations ⋮ Numerical solution of singular integral equations via initial value methods ⋮ Rational function approximations in the numerical solution of Cauchy-type singular integral equations ⋮ The use of spline-on-spline for the approximation of Cauchy principal value integrals ⋮ On the solution of a special kind of singular integral equation ⋮ Piecewise cubic interpolatory polynomials and approximate solution of singular integral equations ⋮ Solving singular integral equations via (0,2,3) lacunary interpolation ⋮ Numerical treatment of solving singular integral equations by using sinc approximations ⋮ Spline approximations for Cauchy principal value integrals ⋮ Interactions of two arbitrarily oriented cracks in a homogeneous anisotropic medium ⋮ A review of linear and nonlinear Cauchy singular integral and integro-differential equations arising in mechanics ⋮ Spline collocation for singular integro-differential equations over (0,1) ⋮ Approximate solution of first kind singular integral equation with generalized kernel using Legendre multiwavelets ⋮ A piecewise linear quadrature of Cauchy singular integrals ⋮ On the solvability of singular integral equations via gauss-jacobi quadrature

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The crack energy and the stress intensity factor for a cruciform crack deformed by internal pressure
• Numerical integration methods for the solution of singular integral equations
• The Numerical Solution of Singular Integral Equations over $( - 1,1)$
• The Numerical Solution of Fredholm integral Equations of the Second Kind
• Approximate Solutions of Systems of Singular Integral Equations
• A PRESSURIZED CRACK IN THE FORM OF A CROSS
• The Numerical Evaluation of the Cauchy Transform on Simple Closed Curves