Optimal approximation techniques for solving Hadamard type integral equations

Abstract

This paper discusses the frequent occurrence of the Hadamard type integral equation of the first kind in solving problems in aerodynamics, fluid dynamics, wave propagation theory, and ecology. Since the exact solution of this equation is also expressed by an integral, the problem of constructing an optimal quadrature formula for its approximate calculation is considered. The analytical form of the coefficients of the optimal quadrature formula is found.