Spectral collocation method for convection-diffusion equation

Spectral collocation method, named linear barycentric rational interpolation collocation method (LBRICM), for convection-diffusion (C-D) equation with constant coefficient is considered. We change the discrete linear equations into the matrix equation. Different from the classical methods to solve the C-D equation, we solve the C-D equation with the time variable and space variable obtained at the same time. Furthermore, the convergence rate of the C-D equation by LBRICM is proved. Numerical examples are presented to test our analysis.