Central Part Interpolation Schemes for Integral Equations

In a weakly singular integral equation of the second kind, we perform a smoothing change of variables and solve the resulting equation either by the collocation or by the product integration method based on a “central part” interpolation by polynomials on the uniform grid. Optimal convergence order of both methods is established. The latter method is hopeful due to especially simple and cheap assembling of the algebraic system of equations.