SAMS Subject Classification Number: 3,23

The novelty of this work rests upon the use of the domain decomposition technique in time variable when discretizing the domain of solution in spectral collocation algorithm. The single domain multivariate spectral collocation-based methods have been proven to be effective in solving time-dependent partial differential equations (PDEs) defined over small time domains. However, there is a significant loss of accuracy as time computational domain proliferates and also when the number of grid points approaches a definite particular number. Therefore, the establishment of the new innovative multi-domain multivariate spectral quasilinearisation method (MDMV-SQLM) is described for the purpose of solving (2+1) dimensional nonlinear PDEs defined on large time intervals. The main output of this study is confirmation that minimizing the size of time computational domain at each subinterval assures sufficiently accurate results that are attained using minimal number of nodal points and less computational time. To highlight the efficiency and accuracy of the MDMV-SQLM, error estimates, condition numbers and computational time are presented for well known (2+1) dimensional nonlinear Burger’s PDEs. The adoption of the domain decomposition technique is effective in suppressing the numerical challenges linked to large matrices and ill-conditioned nature of the resulting coefficient matrix. Also, the obtained results confirm that the numerical scheme is computationally cheap, fast and yield extremely accurate and stable results using fewer number of grid points for large time domains.