A LARGE PARAMETER SPECTRAL PERTURBATION METHOD FOR NONLINEAR SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS THAT MODELS BOUNDARY LAYER FLOW PROBLEMS

In this paper, a new approach for solving coupled systems of nonlinear boundary layer partial differential equations that are defined over a large time interval is presented. The method, called the large parameter spectral perturbation combines asymptotic analysis, and the Chebyshev spectral collocation method. The LSPM is based on using the Chebysev spectral collocation method to solve the sequence of differential equations generated by the asymptotic series approximation. The LSPM is tested on a coupled three-equation system that models the problem of natural convection heat transfer flow past a magnetized vertical permeable plate for liquid metals. The accuracy of the LSPM is tested against the multi-domain bivariate spectral quasilinearisation method (MD-BSQLM) which is an approach that is based on applying the quasilinearisation technique to simplify the nonlinear PDEs first and thereafter decomposing the time domain into smaller non-overlapping sub-intervals which are discretized using the spectral collocation method. The MD-BSQLM combines the accuracy, computational efficiency of spectral method together with guaranteed fast convergence of the approximate solution to the required solution. The approximate numerical result shows that the LSPM is an accurate and computationally efficient method for solving coupled nonlinear systems of PDEs defined over a large time interval. The obtained results are presented in graphical and tabular forms. We remark also, that this study corrects the published test equations by giving the correct transformation, transformed equations and expansion.