Solving of differential equations systems in the presence of fractional derivatives using the orthogonal polynomials
Date
2017-06-15
Journal Title
Journal ISSN
Volume Title
Publisher
Lviv Politechnic Publishing House
Abstract
Побудовано математичну модель руху газу в трубопроводах для випадку, коли не-
усталений процес описано похiдною дробового порядку за часовою змiнною. Сфор-
мульовано крайову задачу. Рiшення задачi знаходять спектральним методом в бази-
сах многочленiв Чебишева–Лагерра за часовою змiнною та многочленiв Лежандра за
координатою. Знаходження рiшення в результатi зведено до системи алгебраїчних
рiвнянь. Проведено числовий експеримент.
The mathematical model of the gas motion in the pipelines for the case where unstable process is described by the fractional time derivative is constructed in the paper. The boundary value problem is formulated. The solution of the problem is founded by the spectral method on Chebyshev-Laguerre polynomials bases with respect to the time variable and Legendre polynomials with respect to the coordinate variable. The finding of the solution eventually is reduced to the system of algebraic equations. The numerical experiment is conducted.
The mathematical model of the gas motion in the pipelines for the case where unstable process is described by the fractional time derivative is constructed in the paper. The boundary value problem is formulated. The solution of the problem is founded by the spectral method on Chebyshev-Laguerre polynomials bases with respect to the time variable and Legendre polynomials with respect to the coordinate variable. The finding of the solution eventually is reduced to the system of algebraic equations. The numerical experiment is conducted.
Description
Keywords
математична модель, рух газу в трубопроводах, спектральні методи, ортогональні многочлени, mathematical model, gas motion in pipelines, spectral methods, orthogonal polynomials
Citation
Pyanylo Ya. Solving of differential equations systems in the presence of fractional derivatives using the orthogonal polynomials / Ya. Pyanylo, O. Bratash, G. Pyanylo // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 4. — No 1. — P. 87–95.