https://doi.org/10.1140/epjp/i2018-11859-5
Regular Article
Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium
1
Department of Computer Sciences, Shahid Beheshti University, G.C. Tehran, Iran
2
Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, G.C. Tehran, Iran
* e-mail: k_parand@sbu.ac.ir
Received:
29
November
2017
Accepted:
5
January
2018
Published online:
31
January
2018
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 
. 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, 
, is obtained as 
for 
. Comparing to the best result obtained so far, it is accurate up to 36 decimal places.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018
