A series-form solution of the coupled nonlinear equations by the method of directly defined inverse mapping and SRM

We derive a series-form solution of the coupled nonlinear equations by the method of directly defined inverse mapping (MDDIM) and spectral relaxation method (SRM). Then, via the method of directly defined inverse mapping with the series-form solution firstly reported in this paper, we can obtain the theoretical and approximate analytical solution that is laid out to explore the features of boundary layer analysis of the nanofluid flow due to a bidirectional stretching sheet under magnetic field along with thermal radiation. Three water-based nanofluids with nanoparticles of Al₂O₃, TiO₂ and CuO play an important role in the solutions. Based on the MDDIM and SRM, the convergence and accuracy of the proposed problems are illustrated, which exhibit meaningful structures. We has been proposed the convergence controlling relaxation parameter ((Formula presented.)) with the help of which the convergence rate and accuracy of the MDDIM are highly improved.