Numerical Algorithms

, Volume 77, Issue 4, pp 1199–1211 | Cite as

A method of directly defining the inverse mapping for solutions of coupled systems of nonlinear differential equations

  • Mathew Baxter
  • Mangalagama Dewasurendra
  • Kuppalapalle Vajravelu
Original Paper


Recently, Liao introduced a new method for finding analytical solutions to nonlinear differential equations. In this paper, we extend this idea to nonlinear systems. We study the system of nonlinear differential equations that governs nonlinear convective heat transfer at a porous flat plate and find functions that approximate the solutions by extending Liao’s Method of Directly Defining the Inverse Mapping (MDDiM).


Method of directly defining the inverse mapping Nonlinear systems Fluid flow Heat transfer Analytical methods Homotopy analysis method 


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The authors thank Professor Shijun Liao for the constructive comments (on the first draft of the paper) which led to definite improvement in the paper. The authors thank the reviewers for constructive comments that led to definite improvement in the paper.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Mathew Baxter
    • 2
  • Mangalagama Dewasurendra
    • 1
  • Kuppalapalle Vajravelu
    • 1
  1. 1.Department of MathematicsUniversity of Central FloridaOrlandoUSA
  2. 2.Department of MathematicsFlorida Gulf Coast UniversityFort MyersUSA

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