Search academic texts

Information × Registration Number 0212U004179, 0107U000365 , R & D reports Title Development of methods and algorithms for solving specific direct and inverse problems for partial differential equations with applying to technical, biological and economical systems. popup.stage_title Head Voitovich Mykola Mykolayovych, Gafiychuk Vasyl Vasylovych, Registration Date 31-01-2012 Organization Pidstryhach Institute of Applied Problems of Mechanics and Mathematics NAS of Ukraine popup.description2 Subject of investigation: nonlinear two-parametric spectral problems, nonlinear system of equations with fractional derivatives, inverse problems of wave field theory, scattering problems on small particles. Goal of work: development of methods and algorithms for solving direct and inverse problems for equations with partial derivatives arising in technical, biological and economical applications. Main results: The methods for determination of associated components of spectrum for two-dimensional nonlinear spectral problems arising in the theory of ordinary differential equations are developed. The existence conditions for associated components of spectrum, which are realized by solving the respective Cauchy problem for differential equation of the first order, are substantiated. Method for calculation of exact derivatives of the matrix determinant in the algorithms for solving two-dimensional nonlinear spectral problems is proposed, and its convergence is established. Two actual inverse problems of the wave field theory are considered. The first one consists in determination of the surface complex impedance providing zero backscattering. For the case of unlimited cylindrical bodies, the problem is reduced to system of two nonlinear two-dimensional integral equations of specific form. The method is approved on the elliptical cylinder. The second problem consists in reconstruction of the shape of the irregular waveguide cross-section in order to recognize the form of the human ear outside canal. The method is approved by numerical experiments for the two-dimensional scalar problem. The analytical-numerical investigation of scattering problems on the small bodies is performed, and method for creation of media with desired acoustic or electromagnetic performances is developed. The asymptotical solutions of such problems are determined. The obtained numerical results confirm the theoretical conclusions and testify about engineering possibility to create the media with the spatial non-homogeneous properties, namely the refraction coefficient and magnetic permeability. Classification of main types of the nonlinear evolutional problems with fractional differential operators is realized, the numerical methods and algorithms for solving above problems are developed, and spatial-time evolution in the nonlinear systems with fractional derivatives is investigated using the numerical modeling. New numerical methods for investigation of the nonlinear solutions to systems of equations with ordinary and fractional derivatives are proposed. Product Description popup.authors Андрійчук М.І. Булацик О.О. Васюник З.І. Войтович М.М. Гісь О.М. Гафійчук В.В. Дацко Б.Й. Заморська О.Ф. Котлярчук Б.К. Кусий О.В. Мелешко В.В. Микитюк І.В. Павлюк В.С. Панасюк А.В. Подлевський Б.М. Процах Л.П. Савенко П.О. Соляр Т.Я. Ткач. М.Д. Тополюк Ю.П. popup.nrat_date 2020-04-02 Close