This book consists of two main parts. In the first part (chapters 1, 2) the authors deal with the problem of searching for signals in a multi-channel system with the help of methods of the Markov and semi-Markov process theory. The second part (chapters 3, 4) deals with numerical-analytical methods of solution of complex integral equations related to results of analysis of the searching problem. In the first chapter the optimal strategy of searching for signals in a multi-channel system is constructed and the corresponding estimate of the search efficiency is found. The second chapter deals with the sub-optimal strategy of searching for signals in a multi-channel system. The authors use the so-called “phase enlargement method” which makes it possible to simplify the corresponding analytic calculations. In the third chapter the iterative spline-quadrature method of solution of integral equations is applied to solution the Fredholm integral equations, the Volterra integral equations, nonlinear Hammerstein integral equations, two-dimensional integral equations with variable bounds. Chapter four deal with the numerical-analytical solutions of integral equations by the spline-iteration method. Solutions of the Volterra and Fredholm integral equations are analysed. Convergence of the spline-iteration and iterative spline-quadrature methods of solution of integral equations is investigated. An estimate of the approximation error is analysed. The book is of interest for researchers and post-graduate students involved in application of the spline-iteration and iterative spline-quadrature methods of solution of integral equations.
Reviewer: Mikhail P. Moklyachuk (Kyïv)