An Accurate Numerical Method for Solving Unsteady Isothermal Flow of a Gas Through a Semi-Infinite Porous Medium

作者：Parand Kourosh^*; Delkhosh Mehdi

来源：Journal of Computational and Nonlinear Dynamics, 2018, 13(1): 011007.

DOI：10.1115/1.4037225

The Kidder equation, y ''(x) + 2xy'(x)/root 1-beta y(x) = 0, x is an element of[0, infinity), beta is an element of[0, 1] with y(0) = 1, and y(infinity) = 0, is a second-order nonlinear two-point boundary value ordinary differential equation ( ODE) on the semi-infinite domain, with a boundary condition in the infinite that describes the unsteady isothermal flow of a gas through a semi-infinite micro-nano porous medium and has widely used in the chemical industries. In this paper, a hybrid numerical method is introduced for solving this equation. First, by using the method of quasi-linearization, the equation is converted to a sequence of linear ODEs. Then these linear ODEs are solved by using the rational Legendre functions (RLFs) collocation method. By using 200 collocation points, we obtain a very good approximation solution and the value of the initial slope y'(0) = -1.19179064971942173412282860380015936403 for beta = 0.50, highly accurate to 38 decimal places. The convergence of numerical results is shown by decreasing the residual errors when the number of collocation points increases.

• 出版日期2018-1