Optimal quadrature formulas in Sobolev space for solving the generalized Abel integral equation
Bakhtiyor Daliyev, Dadakhon Tukxtasinov, Bakhromjon Bozarov, Salim Sabirov, Jamoliddin Abdullayev, Makhfuza Ruzimatova
Abstract
In this article, a composite optimal quadrature formula is constructed for an approximate analytical solution of the generalized integral Abel equation in the Sobolev functional space. The optimal coefficients of this quadrature formula have been found. In addition, using the constructed composite optimal quadrature formula, numerical results of examples of the generalized Abel integral equation were obtained and compared with the exact solution.
Topics & Concepts
Sobolev spaceQuadrature (astronomy)MathematicsIntegral equationMathematical analysisSpace (punctuation)Applied mathematicsPure mathematicsPhysicsComputer scienceOpticsOperating systemIterative Methods for Nonlinear EquationsMathematical functions and polynomialsAlgebraic and Geometric Analysis