Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium

• Published in: European physical journal plus 2018-01, Vol.133 (1), p.28, Article 28
• Main Authors: Parand, Kourosh, Latifi, Sobhan, Delkhosh, Mehdi, Moayeri, Mohammad M.
• Format: Article
• Language: English
• Subjects: Accuracy; Algebra; Applied and Technical Physics; Approximation; Atomic; Boundary conditions; Collocation methods; Complex Systems; Condensed Matter Physics; Decomposition; Differential equations; Engineering; Investigations; Mathematical and Computational Physics; Methods; Molecular; Numerical analysis; Optical and Plasma Physics; Ordinary differential equations; Partial differential equations; Physics; Physics and Astronomy; Porous materials; Porous media; Regular Article; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/i2018-11859-5

. In the present paper, a new method based on the Generalized Lagrangian Jacobi Gauss (GLJG) collocation method is proposed. The nonlinear Kidder equation, which explains unsteady isothermal gas through a micro-nano porous medium, is a second-order two-point boundary value ordinary differential equation on the unbounded interval [ 0 , ∞ ) . Firstly, using the quasilinearization method, the equation is converted to a sequence of linear ordinary differential equations. Then, by using the GLJG collocation method, the problem is reduced to solving a system of algebraic equations. It must be mentioned that this equation is solved without domain truncation and variable changing. A comparison with some numerical solutions made and the obtained results indicate that the presented solution is highly accurate. The important value of the initial slope, y ( 0 ) , is obtained as - 1 . 191790649719421734122828603800159364 for η = 0 . 5 . Comparing to the best result obtained so far, it is accurate up to 36 decimal places.