Abstract
Nonlinear partial differential equations (PDEs) modelling unsteady boundary-layer flows are solved by the spectral relaxation
method (SRM) and the spectral quasilinearization method (SQLM). The SRM and SQLM are Chebyshev pseudospectral based
methods that have been successfully used to solve nonlinear boundary layer flow problems described by systems of ordinary
differential equations. In this paper application of these methods is extended, for the first time, to systems of nonlinear PDEs that
model unsteady boundary layer flow. The new extension is tested on two problems: boundary layer flow caused by an impulsively
stretching plate and a coupled four-equation system that models the problem of unsteady MHD flow and mass transfer in a porous
space. Numerous simulation experiments are conducted to determine the accuracy and compare the computational performance
of the proposed methods against the popular Keller-box finite difference scheme which is widely accepted as being one of the ideal
tools for solving nonlinear PDEs that model boundary layer flow problems. The results indicate that the methods are more efficient
in terms of computational accuracy and speed compared with the Keller-box.