"Optimal quadrature formulas for approximate solution of the rst kind singular integral equation with Cauchy kernel"
", D.M. Akhmedov, Kholmat Shadimetov
Abstract
"In the present paper in $L_2^{(m)}(-1,1)$ space the optimal quadrature formulas with derivatives are constructed for approximate solution of a singular integral equation of the first kind with Cauchy kernel. Approximate solution of the singular integral equation is obtained applying the optimal quadrature formulas. Explicit forms of coefficients for the of optimal quadrature formulas are obtained. Some numerical results are presented."
Topics & Concepts
MathematicsQuadrature (astronomy)Mathematical analysisSingular integralGauss–Kronrod quadrature formulaIntegral equationNyström methodClenshaw–Curtis quadratureCauchy distributionGauss–Jacobi quadratureTanh-sinh quadratureNumerical integrationKernel (algebra)Cauchy problemGaussian quadratureApplied mathematicsInitial value problemPure mathematicsPhysicsOpticsIterative Methods for Nonlinear EquationsMathematical functions and polynomialsElectromagnetic Scattering and Analysis