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On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows

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  • S. S. Motsa

Abstract

This work presents a new approach to the application of the spectral homotopy analysis method (SHAM) in solving non‐linear partial differential equations (PDEs). The proposed approach is based on an innovative idea of seeking solutions that obey a rule of solution expression that is defined in terms of bivariate Lagrange interpolation polynomials. The applicability and effectiveness of the expanded SHAM approach are tested on a non‐linear PDE that models the problem of unsteady boundary layer flow caused by an impulsively stretching plate. Numerical simulations are conducted to generate results for the important flow properties such as the local skin friction. The accuracy of the present results is validated against existing results from the literature and against results generated using the Keller‐box method. The preliminary results from the proposed study indicate that the present method is more accurate and computationally efficient than more traditional methods used for solving PDEs that describe nonsimilar boundary layer flow.

Suggested Citation

  • S. S. Motsa, 2014. "On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:848170
    DOI: 10.1155/2014/848170
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    References listed on IDEAS

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    1. Shijun Liao, 2012. "Homotopy Analysis Method in Nonlinear Differential Equations," Springer Books, Springer, number 978-3-642-25132-0, March.
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    Cited by:

    1. S. S. Motsa, 2014. "On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Sandile S. Motsa & Zodwa G. Makukula, 2017. "On a Bivariate Spectral Homotopy Analysis Method for Unsteady Mixed Convection Boundary Layer Flow, Heat, and Mass Transfer due to a Stretching Surface in a Rotating Fluid," Journal of Applied Mathematics, John Wiley & Sons, vol. 2017(1).

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