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Numerical Algorithms

, Volume 61, Issue 3, pp 515–524 | Cite as

Unique and multiple PHAM series solutions of a class of nonlinear reactive transport model

  • Hossein Vosoughi
  • Elyas ShivanianEmail author
  • Saeid Abbasbandy
Original Paper

Abstract

The purpose of this paper is to visit a class of nonlinear reactive transport model in the case including advective and diffusive transport with the Michaelis-Menten reaction term. We apply the method so-called predictor homotopy analysis method (PHAM) which has been recently proposed to predict multiplicity of solutions of nonlinear BVPs. Consequently two consequential matters are indicated which confirms the authority of PHAM to identify multiple solutions: (i) The Talylor series solutions are improved by the so-called convergence-controller parameter (ii) The possibility of existence of multiple solutions is discovered in some cases for the model.

Keywords

Predictor homotopy analysis method Rule of multiplicity of solutions Prescribed parameter  Reactive transport model 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Hossein Vosoughi
    • 1
  • Elyas Shivanian
    • 2
    Email author
  • Saeid Abbasbandy
    • 2
  1. 1.Department of Mathematics, Faculty of ScienceIslamshahr Branch, Islamic Azad UniversityTehranIran
  2. 2.Department of MathematicsImam Khomeini International UniversityGhazvinIran

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