Approximate Solution of a Singular Integral Equation Using the Sobolev Method
Kh. M. Shadimetov, D.M. Akhmedov
Abstract
In the present paper in the $$L_{2}^{(m)}(-1,1)$$ 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 for the singular integral equation is obtained, applying the optimal quadrature formulas (OQF). Explicit forms of coefficients for the optimal quadrature formulas are obtained. Some numerical results are presented.
Topics & Concepts
MathematicsQuadrature (astronomy)Singular integralNyström methodMathematical analysisIntegral equationSobolev spaceSingular solutionKernel (algebra)Gauss–Kronrod quadrature formulaApplied mathematicsPure mathematicsEngineeringElectrical engineeringNumerical methods in engineeringDifferential Equations and Boundary ProblemsDifferential Equations and Numerical Methods