Preface -- 1. Complex and Real Algebras -- 2. Integral Operators. Smooth Curves -- 3. Riemann-Hilbert Problem -- 4. Piecewise Smooth and Open Contours -- 5. Muskhelishvili Equation -- 6. Numerical Examples -- Bibliography.

This book deals with numerical analysis for certain classes of additive operators and related equations, including singular integral operators with conjugation, the Riemann-Hilbert problem, Mellin operators with conjugation, double layer potential equation, and the Muskhelishvili equation. The authors propose a unified approach to the analysis of the approximation methods under consideration based on special real extensions of complex C*-algebras. The list of the methods considered includes spline Galerkin, spline collocation, qualocation, and quadrature methods .