Environmental Modeling & Assessment

, Volume 24, Issue 1, pp 109–120 | Cite as

On Use of Expanding Parameters and Auxiliary Term in Homotopy Perturbation Method for Boussinesq Equation with Tidal Condition

  • Selva Balaji Munusamy
  • Anirban DharEmail author


This paper uses the homotopy perturbation method for the analytical solution of groundwater table fluctuations, in response to the tidal boundary condition, for a coastal unconfined aquifer with sloping beach face. The Boussinesq equation for sloping beach contains two non-linear terms. The governing equation is reconstructed in homotopic form with two virtual perturbation parameters and an auxiliary term. The secular terms generated from the non-linear diffusion term and the slope term are eliminated by using parameter expansions based on two virtual parameters. Two non-dimensional parameters emerge from the solution in the process of eliminating secular terms: (i) parameter equivalent to amplitude parameter and (ii) parameter representing beach slope. The second-order (starting from zeroth-order) solution is presented. The higher-order solution efficiently captures the non-linearity of the problem.


Homotopy perturbation method Secular term Non-linearity Auxiliary term Approximate solution 


Funding Information

This study is supported by Science and Engineering Research Board (Grant Number: SB/FTP/ETA-0356/2013) under the Department of Science and Technology, Government of India.

Supplementary material

10666_2018_9636_MOESM1_ESM.tex (8 kb)
(TEX 7.82 KB)


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Indian Institute of Technology KharagpurKharagpurIndia

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