GENERALIZED JACOBI RATIONAL SPECTRAL METHODS WITH ESSENTIAL IMPOSITION OF NEUMANN BOUNDARY CONDITIONS IN UNBOUNDED DOMAINS

In this paper, we develop several generalized Jacobi rational spectral methods with essential imposition of Neumann boundary conditions for one/two dimensional Neumann problems. Some basic results on the generalized Jacobi rational approximations for Neumann problems are established, which play important roles in the related spectral methods. Three model problems are considered. The convergence of proposed schemes is proved. Numerical results demonstrate their spectral accuracy and efficiency.