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The modified decomposition method applied to unsteady flow of gas through a porous medium. (English) Zbl 1024.76056

Summary: We construct an analytic solution for unsteady gas flow through a porous medium described by the nonlinear ordinary differential equation \[ y''(x)+ {2x\over\sqrt {1-\alpha y}}y'(x)=0,\quad 0< \alpha <1,\;y(0)=1, \quad \lim_{x\to\infty} y(x)=0. \] Our approach rests on a modification of Adomian decomposition method. The diagonal Padé approximants are used in the analysis to capture the essential behavior of \(y(x)\) and to determine the initial slope \(y'(0)\). The proposed scheme avoids the complexity provided by using perturbation techniques.

MSC:

76S05 Flows in porous media; filtration; seepage
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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References:

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