| DC Field | Value | Language |
|---|
| dc.contributor.author | Pyanylo, Ya. | - |
| dc.contributor.author | Sobko, V. | - |
| dc.date.accessioned | 2018-07-12T07:56:07Z | - |
| dc.date.available | 2018-07-12T07:56:07Z | - |
| dc.date.issued | 2016 | - |
| dc.identifier.citation | Pyanylo Ya. Pipeline pressure distribution finding methods / Ya. Pyanylo, V. Sobko // Mathematical Modeling and Сomputing. – 2016. – Volume 3, number 2. – Р. 199–207. – Bibliography: 21 titles. | uk_UA |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/42391 | - |
| dc.description.abstract | The method of solving problems of mathematical physics, in particular for calculating a non-stationary gas flow in pipelines, is proposed in this article on the basis of the biorthogonal polynomial constructed by the authors. The method of solving the problem by means of the separation of variables in the base of biorthogonal polynomials is investigated. The analytical-approximate and approximate solutions of the problem as the sum of some biorthogonal and quasi-spectral polynomials are found. The comparative analysis between the obtained analytical-approximate and approximate solutions is conducted. The influence of parameters of methods, including the order of the partial sum, a bit grid, and an accuracy error of calculations on the obtained solution are studied. The results of calculation are presented in the form of tables. У працi на базi побудованих авторами бiортогональних полiномiв запропоновано метод розв’язування задач математичної фiзики, зокрема для розрахунку нестацiонарного руху газу в трубопроводах. Дослiджено спосiб розв’язування задачi методом роздiлення змiнних у базисi бiортогональних полiномiв. Знайдено аналiтично-наближений та наближений розв’язки задачi у виглядi суми ряду бiортогональних та квазiспектральних полiномiв. Проведено порiвняльний аналiз мiж отриманими наближеним та аналiтично-наближеним розв’язками. Вивчено вплив параметрiв методiв, зокрема порядку часткової суми, розрядної сiтки та похибки обчислення на точнiсть отриманого розв’язку. Результати обчислень подано у виглядi таблиць. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.subject | spectral methods | uk_UA |
| dc.subject | mathematical model | uk_UA |
| dc.subject | non-stationary gas flow | uk_UA |
| dc.subject | linearization | uk_UA |
| dc.subject | biorthogonal and quasi-orthogonal polynomials | uk_UA |
| dc.subject | спектральнi методи | uk_UA |
| dc.subject | математична модель | uk_UA |
| dc.subject | нестацiонарний рух газу | uk_UA |
| dc.subject | лiнеаризацiя | uk_UA |
| dc.subject | бiортогональнi та квазiортогональнi полiноми | uk_UA |
| dc.title | Pipeline pressure distribution finding methods | uk_UA |
| dc.title.alternative | Методи знаходження розподiлу тиску в трубопроводi | uk_UA |
| dc.type | Article | uk_UA |
| dc.contributor.affiliation | Centre for Mathematical Modelling of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine | uk_UA |
| dc.coverage.country | UA | uk_UA |
| dc.format.pages | 199–207 | - |
| dc.relation.references | [1] АbramovichМ., Stygan I. Reference book of Special Functions with Formulae, Diagrams and Mathematical Tables. Мoscow, Science (1979). [2] GletcherК. Numerical Methods of the Base of the Galierkin’s Method. Мoscow, World (1988). [3] DziadykV.К. Аpproximate Methods of Solution of Differential and Integral Equations. Кyiv, Scientific Thought (1998). [4] DziadykV.К. Introduction in to the Theory of Uniform Approximation of Functions by Polynomials. Мoscow, Science (1977). [5] Каntorovich L.V., АkilovG.P. Functional Analysis. Мoscow, Science (1984). [6] КorneychukN.P. Accurate Constants in the Theory of Approximation. Мoscow, Science (1987). [7] LаntsoshК. Practical Methods of Applied Analysis. Moscow, State Publishing House of Physical- Mathematical Literaure (1961). [8] DitkinV.А., PrudnikovА.P. Оperational Calculation. Мoscow, Higher School (1975). [9] LopukhN., PritulaМ., PjanyloYa., SavulaYa. Algorithms of Calculation of Hydrodynamical Parameters of Gas Flow in Pipelines. Visnyk of Lviv University. Serie of Appl. Math. and Comp. Sci, 12, 108–117 (2007) (in Ukrainian). [10] PyanyloYa.D., SobkoV.G. Building and Research of Biorthogonal Polynomials on the Base of the Cheby- shev Polynomials. Appl. Problems of Mech. and Math. 11, 135–141 (2013) (in Ukrainian). [11] PyanyloYa., SobkoV. Research of Peculiarities of Spectral Schedules in the Bases of Orthogonal, Quaziorthogonal, Biorthogonal Polynomials. Phisical-Mathematical Modelling and Information Techolo- gies. 19, 146–156 (2014) (in Ukrainian). [12] Ghoreishi F., Mohammad Hosseini S. The Tau method and a new preconditioner. J. Comp. Appl. Math. 163(2), 351–379 (2004). [13] Coutsias E.A., HagstormT., Hesthaven J. S., TorresD. Integration preconditioners for differential opera- tors in spectral τ-methods. Proc. 3rd International Conference on Spectral and High Order Methods, Houston, TX, 21–38 (1995). [14] BernardiC., MadayY. Properties of some weighted sobolev spaces, and applications to spectral approxi- mations. SIAM J. Numer. Anal. 26, 769–829 (1989). [15] Jie Shen. Efficient spectral-Galerkin method II. Direct solvers for second- and fourthorder equations by using Chebyshev polynomials. SIAM J. Sci. Comput. 16, 74–87 (1995). [16] Jie Shen. Efficient Chebyshev-Legendre Galerkin methods for elliptic problems. In A.V. Ilin and R. Scott, editors, Proceedings of ICOSAHOM’95. Houston. J. Math. 233–240 (1996). [17] BadkovV.M. Convergence in the mean and almost everywhere of Fourier series in polynomials orthogonal on an interval. Math. USSR Sbornik. 2, MR0355464 (50:7938) 223–256 (1974). [18] JohnP. Boyd. Chebyshev and Fourier Spectral methods, 2nd edition. Dover Publication, Inc., Mineola, New York (2001). [19] WalteA. Strauss. Partial Differential Equations: An Introduction, 2nd edition, John Wiley and Sons (2008). [20] CabosCh. A preconditioning of the tau operator for ordinary differential equations. Z. Angew. Math. Mech. 74 (11), 521–532 (1994). [21] Coutsias E.A., HagstormT., Hesthaven J., TorresD. Integration preconditioners for differential operators in spectral τ-methods. Proc. 3rd International Conference on Spectral and High Order Methods, Houston, TX, 21–38 (1995). | uk_UA |
| dc.citation.journalTitle | Mathematical Modeling and Сomputing | - |
| dc.subject.udc | 519.6:539.3 | uk_UA |
| Appears in Collections: | Mathematical Modeling And Computing. – 2016. – Vol. 3, No. 2
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