Open AccessA collocation method for the Williams equation with Chebyshev polynomials
Author(s) -
O. V. Germider,
В. Н. Попов
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2056/1/012005
Subject(s) - chebyshev polynomials , chebyshev equation , mathematics , collocation (remote sensing) , orthogonal collocation , mathematical analysis , boundary (topology) , reflection (computer programming) , flow (mathematics) , chebyshev filter , collocation method , boundary value problem , plane (geometry) , orthogonal polynomials , geometry , classical orthogonal polynomials , differential equation , computer science , ordinary differential equation , machine learning , programming language
The linearized problem of gas flow in plane channel with infinite walls has been solved in the kinetic approximation. The flow in the channel is caused by a constant pressure gradient parallel to the walls of the channel. The Williams equation has been used as a basic equation, and the boundary condition has been set in terms of the diffuse reflection model. The collocation method for Chebyshev polynomials has been applied to construct the solution of the equation of Williams with the given boundary conditions. The mass flux of the gas in the channel has been calculated.