Approximate analytical solutions to thermo-poroelastic equations by means of the iterated homotopy analysis method

Abstract

A new approach of the homotopy analysis method (HAM), named iterated homotopy analysis method (I-HAM) is used to find approximate analytical solutions to thermo-poroelastic equations. The homotopy analysis method contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region of the series solution. This method is reliable and manageable. The I-HAM solutions are compared with numerical solutions. To the best of our knowledge, this kind of analytic solutions has been never reported. Also, in each example, the comparison between I-HAM and traditional HAM is done, which shows the efficiency of I-HAM.

Keywords:

• thermo-poroelastic equations
• similarity transformations
• homotopy analysis method
• series solutions
• iterated method

2000 AMS Subject Classifications :

• 65H20
• 65L05
• 65L80
• 74F10
• 80A20

Acknowledgements

The authors would like to thank the anonymous referees and the editor for valuable suggestions.