# Collocation method applied to unsteady flow of gas through a porous medium

## Authors

• Subrahamanyam Upadhyay BHU Varanasi India
• K.N. Rai DST-CIMS, BHU, Varanasi, India

2014-07-06

## Abstract

In this article, we study a two point boundary value problem of non linear differential equation on a semi infinitedomain that describes the unsteady flow of gas through a porous medium. Under special transform, we convert thisproblem to boundary value problem in compactly supported domain [0,1]. An algorithm provided for obtainingsolution by Legendre wavelet collocation method. This method is effectively used to determine y (t) and its initialslope at the origin. The convergence and stability analysis is provided. The results thus obtained are compared withthe those obtained from modified decomposition method [5], Variational iterational method [6], rational Chebyshevfunctions method (RCM) [7] and radial basis function (RBF) collocation method [10]. It has been observed thatthe proposed method provide better results with lesser computational complexity.

Keywords: Convergence and stability analysis, Legendre Wavelets, Legendre wavelet collocation method, Kidder's equation.

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