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Information × Registration Number 0210U004052, 0106U000596 , R & D reports Title Development of iterative method for solving the nonlinear integral equations with branching solutions, nonlinear spectral problems and problems of recognition of objects in the wave field popup.stage_title Head Voytovych Mykola Mykolayovych, Доктор фізико-математичних наук Registration Date 05-02-2010 Organization Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NASU popup.description2 Object of investigation: nonlinear integral equations of Hammerstein type, generalized spectral eigenvalue problems, problems of recognition of objects in the wave field. The aim of investigation: to develop and approve the numerical methods and algorithms for solving nonlinear spectral equations with branching of solutions, nonlinear with respect to spectral parameter (scalar or vector) eigenvalue problems for self-adjoint operators in Hilbert spaces, and the problems of recognition a certain class objects in the wave field. The main results: the solutions described by a finite number of complex parameters, are obtained for one class of nonlinear integral equations of Hammerstein type arising in optimization problems with free phase. These parameters are defined from the system consisting of one integral equation and finite number of transcendental ones. Existence of equivalent groups of solutions of nonlinear integral equations is determined. The necessary conditions for the bifurcation points and the system of equations for their calculation are obtained. Stabilization procedure ensuring the convergence of minimizing sequences in optimization problems with free phase with disturbed operators is proposed and justified. Sufficient convergence conditions for gradient methods are established. Numerical algorithms for solving linear and nonlinear twoparametrical (multiparametrical) eigenvalue problems, in particular, new modification of the algorithm of constructing the eigenvalue curves, linear and nonlinear with respect to spectral parameters of twoparametrical eigenvalue problems, enabling to find all real eigenvalue curves in the given region of changing the spectral parameters of problem, were proposed. The generalized method for solving nonlinear vector spectral problem for the case of holomorphic operator-functions, that allows finding the connected spectrum components, was developed. Using the implicit functions theory to two-dimensional nonlinear spectral problems, the conditions of existence of connected spectrum components were established, and the algorithm for their determination by means of the appropriate Cauchy problem for differential equation of the first order, was developed. The algorithms for solving inverse problems of the object shape recognition in the wave field according to the measured scattering patterns at the resonant frequencies, and recognition of the boundary form of nonregular waveguide according to measured amplitudes of eigen waves in its output, were developed and realized. Product Description popup.authors Андрійчук Михайло Іванович Подлевський Богдан Михайлович Савенко Петро Олександрович popup.nrat_date 2020-04-02 Close