Approximate Analytical Solution of Non-Linear Boussinesq Equation for the Unsteady Ground Water Flow in an Unconfined Aquifer by Homotopy Perturbation Transform Method

Applied Mathematics and Sciences: An International Journal (MathSJ) - H-Index - 9

ISSN: 2349 - 6223 

http://airccse.com/mathsj/index.html

Approximate Analytical Solution of Non-Linear Boussinesq Equation for the Unsteady Ground Water Flow in an Unconfined Aquifer by Homotopy Perturbation Transform Method

Deepti Mishra, Vikas Pradhan and Manoj Mehta

LDRP Institute of Technology & Research , Ganddhinagar, India

Department of Applied Mathematics & Humanities, S.V.N.I.T, Surat 395007, India

Abstract

For one dimensional homogeneous, isotropic aquifer, without accretion the governing Boussinesq equation under Dupuit assumptions is a nonlinear partial differential equation. In the present paper approximate analytical solution of nonlinear Boussinesq equation is obtained using Homotopy perturbation transform method(HPTM). The solution is compared with the exact solution. The comparison shows that the HPTM is efficient, accurate and reliable. The analysis of two important aquifer parameters namely viz. specific yield and hydraulic conductivity is studied to see the effects on the height of water table. The results resemble well with the physical phenomena.

Keywords

Aquifers, stream-aquifer interaction, Dupuit assumptions, Boussinesq equation, Homotopy perturbation

transform method.

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