Constructive methods for the practical treatment of integral equations

The content covers various advanced topics in numerical methods for integral equations. It discusses the error norms of specific Gauss-Quadrature formulas and explores solutions to integral equations on surfaces in space. An adaptive step size control for Volterra integral equations is examined, alongside A(?)-stable mixed Volterra Runge-Kutta methods. Constrained approximation techniques are presented for solving integral equations, and the numerical solution by collocation for Volterra integrodifferential equations with nonsmooth solutions is addressed. The inclusion of regular and singular solutions for certain integral equations is highlighted, along with methods for solving the inverse scattering problem for time-harmonic acoustic waves. The text also delves into optimal discrepancy principles for Tikhonov regularization of integral equations and the spline-Galerkin method for quantum mechanic integral equations. Additional topics include product integration for weakly singular integral equations, stability results for discrete Volterra equations, and the design of acoustic torpedos. It further discusses the condition number of boundary integral equations in acoustic scattering, numerical solutions of singular integral equations related to jet-flapped wings, and Tikhonov-Phillips regularization of the Radon Transform. The content concludes with an analysis of discretization methods for Volterra-type equations and stabilit