Approximate Formulas for Special and Singular Integrals

The monograph is devoted to the construction of quadrature formulas for certain special and singular integrals. Their convergence and the estimation of their residual terms are investigated. Multidimensional cases are considered and studied, i.e., cubature formulas for singular integrals with Cauchy-type kernels are constructed, and their error estimates are provided. The study also examines the importance of approximate calculations of singular integrals for obtaining numerical solutions to singular integral equations in closed form. For ease of use in educational and practical settings, the book includes tables containing coefficients for two-point and one-point quadrature formulas at the end. An extensive literature review related to the monograph's topic is also provided.