https://oldena.lpnu.ua/handle/ntb/42391| Title: | Pipeline pressure distribution finding methods |
| Other Titles: | Методи знаходження розподiлу тиску в трубопроводi |
| Authors: | Pyanylo, Ya. Sobko, V. |
| Affiliation: | Centre for Mathematical Modelling of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine |
| Bibliographic description (Ukraine): | 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. |
| Journal/Collection: | Mathematical Modeling and Сomputing |
| Issue Date: | 2016 |
| Country (code): | UA |
| UDC: | 519.6:539.3 |
| Keywords: | spectral methods mathematical model non-stationary gas flow linearization biorthogonal and quasi-orthogonal polynomials спектральнi методи математична модель нестацiонарний рух газу лiнеаризацiя бiортогональнi та квазiортогональнi полiноми |
| Number of pages: | 199–207 |
| 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. |
| URI: | https://ena.lpnu.ua/handle/ntb/42391 |
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| Content type: | Article |
| Appears in Collections: | Mathematical Modeling And Computing. – 2016. – Vol. 3, No. 2 |
| File | Description | Size | Format | |
|---|---|---|---|---|
| 011-91-99.pdf | 249.82 kB | Adobe PDF | View/Open |
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