Overlapping Multi-domain Bivariate Spectral Method for Systems of Nonlinear PDEs with Fluid Mechanics Applications

An efficient overlapping multi-domain bivariate spectral quasilinearization method (OMD-BSQLM) is introduced for non-similar boundary layer equations arising in fluid mechanics. Previously, the multi-domain approach has been applied to either space or time interval but not both. The new method applies the multi-domain technique in both space and time interval. The time interval is decomposed into non-overlapping sub-intervals, and the space interval is split into overlapping sub-domains. Numerical experiments are carried out to highlight the accuracy and efficiency of the method. An analysis of the convergence and accuracy of the OMD-BSQLM is given using error norms and residual errors. The series solutions are used to validate the accuracy of the OMD-BSQLM results. The new method converges rapidly and gives accurate results after a few iterations and using a few grid points. Moreover, the accuracy does not worsen when a large time domain is considered.