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Registration Number

0225U003732, (0122U200605) , R & D reports

Title

Methods of numerical mathematics for linear and nonlinear boundary value problems and operator equations

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Методи обчислювальної математики для лінійних і нелінійних крайових задач та операторних рівнянь

Head

Hapko Roman S., д.ф.-м.н.

Registration Date

10-08-2025

Organization

Ivan Franko National University of Lviv

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Develop a lot of approximate methods to solve some classes of linear and nonlinear boundary value problems and operator equations by using the boundary integral equations method

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Research report: 144 p., 19 figures, 32 tables, 124 sources. INVERSE OPERATOR APPROXIMATION, GENETIC ALGORITHM, ELLIPTICAL PARTIAL INDEPENDENT EQUATION, DIRICHLE PROBLEM, CAUSHY PROBLEM, CHAIN FRACTIONS, LOCAL CONVERGENCE, L-CURVE METHOD, FUNDAMENTAL SOLUTION METHOD, KHOVANSKY METHOD, NONLINEAR PROBLEM, INVERSE PROBLEM, ONE-SIDED POLYNOMIAL MATRIX EQUATIONS, DIVIDED DIFFERENCE, RADIAL BASIS FUNCTIONS, TIKHONOV REGULARIZATION, HEAT CONDUCTIVITY EQUATION, DIFFERENTIAL METHODS, GENERALIZED LAPLACE EQUATION, LIPSHITSY CONDITIONS, WAVE EQUATION. The purpose of the work is to develop new approximate methods for solving classes of linear and nonlinear boundary value problems and operator equations using the method of boundary integral equations. The subject of the research is effective numerical methods and algorithms for constructing discrete models of correct and incorrect problems of mathematical physics, which can be implemented as an intellectual basis of commercial computer environments for performing qualified computational experiments. Research methods are the method of fundamental sequences, boundary integral equations of various types and dimensions, modifications of the Newton method, systems of matrix-polynomial equations. Approximate schemes for solving stationary and non-stationary problems for partial differential equations, nonlinear functional equations, and systems of second-order matrix equations have been developed.

Product Description

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Beshlei Andrii V.
Borachok Ihor V.
Vavrychuk Vasyl H.
Harasym Yaroslav S.
Muzychuk Yurii A.
Nedashkovska Anastasiia M.
Khapko Roman S.
Yarmola Halyna P.

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2025-08-10