Numerical Algorithms

, Volume 61, Issue 3, pp 499–514

On a new analytical method for flow between two inclined walls

  • Sandile S. Motsa
  • Precious Sibanda
  • Gerald T. Marewo
Original Paper

Abstract

Efficient analytical methods for solving highly nonlinear boundary value problems are rare in nonlinear mechanics. The purpose of this study is to introduce a new algorithm that leads to exact analytical solutions of nonlinear boundary value problems and performs more efficiently compared to other semi-analytical techniques currently in use. The classical two-dimensional flow problem into or out of a wedge-shaped channel is used as a numerical example for testing the new method. Numerical comparisons with other analytical methods of solution such as the Adomian decomposition method (ADM) and the improved homotopy analysis method (IHAM) are carried out to verify and validate the accuracy of the method. We show further that with a slight modification, the algorithm can, under certain conditions, give better performance with enhanced accuracy and faster convergence.

Keywords

Nonlinear equations Exact analytical solutions Successive linearisation method Channel flow 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Sandile S. Motsa
    • 1
  • Precious Sibanda
    • 1
  • Gerald T. Marewo
    • 2
  1. 1.School of Mathematical SciencesUniversity of KwaZulu-NatalPietermaritzburgSouth Africa
  2. 2.Department of MathematicsUniversity of SwazilandKwaluseniSwaziland

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