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.
"On Extending the Quasilinearization Method to Higher Order Convergent Hybrid Schemes Using the Spectral Homotopy Analysis Method." J. Appl. Math. 2013 1 - 9, 2013. https://doi.org/10.1155/2013/879195