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On Extending the Quasilinearization Method to Higher Order Convergent Hybrid Schemes Using the Spectral Homotopy Analysis Method

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  • Sandile S. Motsa
  • Precious Sibanda

Abstract

We propose a sequence of highly accurate higher order convergent iterative schemes by embedding the quasilinearization algorithm within a spectral collocation method. The iterative schemes are simple to use and significantly reduce the time and number of iterations required to find solutions of highly nonlinear boundary value problems to any arbitrary level of accuracy. The accuracy and convergence properties of the proposed algorithms are tested numerically by solving three Falkner‐Skan type boundary layer flow problems and comparing the results to the most accurate results currently available in the literature. We show, for instance, that precision of up to 29 significant figures can be attained with no more than 5 iterations of each algorithm.

Suggested Citation

  • Sandile S. Motsa & Precious Sibanda, 2013. "On Extending the Quasilinearization Method to Higher Order Convergent Hybrid Schemes Using the Spectral Homotopy Analysis Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:879195
    DOI: 10.1155/2013/879195
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    References listed on IDEAS

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    1. Sudhakar G. Pandit, 1997. "Quadratically converging iterative schemes for nonlinear Volterra integral equations and an application," International Journal of Stochastic Analysis, Hindawi, vol. 10, pages 1-10, January.
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    Cited by:

    1. Vikash Kumar Sinha & Prashanth Maroju, 2025. "Numerical solution of coupled Lane–Emden–Fowler type equation by embedded quasilinearization method with homotopy analysis method," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(1), pages 230-240, March.

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