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

  • Kourosh ParandEmail author
  • Sobhan Latifi
  • Mehdi Delkhosh
  • Mohammad M. Moayeri
Regular Article

Abstract.

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 \( [0, \infty)\). 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 \(\eta = 0.5\). Comparing to the best result obtained so far, it is accurate up to 36 decimal places.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Kourosh Parand
    • 1
    • 2
    Email author
  • Sobhan Latifi
    • 1
  • Mehdi Delkhosh
    • 1
  • Mohammad M. Moayeri
    • 1
  1. 1.Department of Computer SciencesShahid Beheshti UniversityG.C. TehranIran
  2. 2.Department of Cognitive Modeling, Institute for Cognitive and Brain SciencesShahid Beheshti UniversityG.C. TehranIran

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