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Information × Registration Number 0224U001867, 0119U100607 , R & D reports Title The development of numerical methods for non-linear integral equations of Hammerstein type, multi-parameter spectral problems and one-dimensional and multidimensional boundary value problems of mathematical physics popup.stage_title Head Andriychuk Mykhaylo I., Доктор технічних наукSavenko Petro O., д.т.н. Registration Date 31-01-2024 Organization Institute of Applied Problems of Mechanics and Mathematics named after Ya. S. Pidstryhach of the National Academy of Sciences of Ukraine popup.description2  Research objects: nonlinear integral equations of the Hammerstein and Urison type, direct and inverse multiparameter spectral problems, high-precision third-order difference schemes, integral transformations for the differential operator, scattering on small inhomogeneities. The purpose of the work is development, substantiation, generalization and testing of numerical methods for solving the non-linear integral equations of the Hammerstein type, multi-parameter spectral problems, non-self-adjoint problems of the generalized method of eigen-oscillations and boundary-value problems on eigenvalues. Main results: A method of studying the problem of non-uniqueness of solutions of a nonlinear integral equation of the Urison type, the kernel of which depends on several numerical parameters, has been developed. The approach is a generalization of the previously developed method of solving nonlinear multiparameter spectral problems for the case of an arbitrary type of nonlinearity in the kernel of the integral equation. An analytical-numerical algorithm for restoring a surface given by an implicit function has been developed. A variational approach to solving linear and nonlinear multiparametric spectral problems in Euclidean space has been developed. Equivalence of spectral and corresponding variational problems is proved. Variational-gradient algorithms for finding generalized eigenvalues and eigenvectors have been constructed. Their local convergence is substantiated. The regularization method was used to correctly find the normal quasi-solution of a nonlinear operator equation of the first kind. The nonlinear operator of the problem is presented in the form of a superposition of a continuous nonlinear operator and a linear completely continuous operator on pairs of complex-valued Hilbert spaces with mean-square metric. The regularization procedure consists in matching the regularization parameter with the error of the problem operator. Product Description popup.authors Yevstyhneiev Borys Ye. Yuriy I. Bilushchak Voitovich Mykola M. Datsko Bohdan Yo. Zamors'ka Ol'ga F. Kutniv Myroslav V. Podlevskyi Bohdan M. Solyar Tetyana Ya. Tkachuk Viktor P. Topoliuk Yurii P. Khomenko Nadiia V. Chernukha Olha Yu. Chuchvara Anastasya E popup.nrat_date 2024-01-31 Close