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

S. S. Motsa | Zendy; Precious Sibanda | Zendy

Open Access

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

Author(s) -

S. S. Motsa,

Precious Sibanda

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/879195

Subject(s) - mathematics , convergence (economics) , homotopy analysis method , embedding , simple (philosophy) , nonlinear system , collocation (remote sensing) , algorithm , iterative method , sequence (biology) , homotopy , boundary value problem , mathematical optimization , computer science , mathematical analysis , philosophy , physics , epistemology , quantum mechanics , artificial intelligence , machine learning , biology , pure mathematics , economics , genetics , economic growth

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

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