The Fully Discrete Legendre And Chebyshev Spectral Method For The Convection-diffusion Equation

The purpose of this paper is to consider spectral numerical approximations to one-dimensional advection-diffusion equation{Ut-vuxx +(bu)x + b0u = f(x,t),x ?A,t?J,u(±1,t)= 0,t ? J,u(x,0)= u0(x),x ? AIn this paper,the Euler implicit scheme for one dimensional convection dif-fusion equation and some properties of the application of the convection diffusion equation are given.In this paper,we give the Legendre spectral method and the Chebyshev spectral format in third and fourth chapters,and the existence and uniqueness of the solution in turn,and the convergence of the near quasi solution and the error estimation to the exact solution.The convection diffusion equation is analyzed in several aspects.