Registration Number
0210U003534,
0108U004150
, R & D reports
Title
Numerical methods of the decision of the differential equations and the integrated equations of mathematical physics and mechanics
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Head
Shynkarenko H. A., Khapko R. S.,
Registration Date
09-02-2010
Organization
Ivan Franko National University of Lviv
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The research unit is boundary value problem in potential theory and Fredholm integral equation of the first kind with weak singularity in the kernel. Mathematical models of appropriate physical phenomenons are also the object if own investigation. The main purpose is the construction and justification of schemes which are the basis of computing experiments in physical and mechanical problems. The latter are described by means of singularly perturbed value and initial boundary value direct and inverse problems for system of partial differential equations. The construction and justification of numerical approaches for mathematical physics and inverse problems solution obtained by integral and nonlinear functional equation method have been also investigated. To solve the above problems we used some methods of mathematical analysis, the theory of numerical method, the theory of differential equation, the finite elements method and the integral equation one We constructed own researches by use integral equations of various kings and dimensions, Laguerre transformation, Green functions, the decomposition of complex irregular domains. The problems of approximate schemes construction, corresponding operators and spaces approximation, stability and convergence have been considered. The numerical schemes to solve inverse problems of cracks, inclusions and boundary value restitution in partially-unbounded domains for Laplace equation, heat equation and Navie system have been constructed. The convergence of iterative process with super quadratic degree of convergence for certain class of nonlinear equations was proved.
Product Description
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Абрамов Є.М.
Гарасим Я.С.
Коковська Я.В.
Малець Р.Б.
Мандзюк Т.С.
Остудін Б.А.
Пахолків Л.Б.
Сінчук Ю.О.
Семенюта Т.А.
Собейко О.
Хапко Р. С.
Чабан Ф.В.
Шахно С.М.
Шинкаренко Г.А.
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2020-04-02
