Spectral Methods For Two Classes Of Boundary Value Problems Of Differential Equations

This paper discusses the application of spectral methods for solving the numerical solution of boundary value problems of two classes of differential equations.For Stokes problem,the Green's theorem is used to convert the constant Stokes problem into a mixed variational form,the existence and uniqueness of solution is obtained by use of the BB condition.In order to derive the discrete solution scheme,we construct the space of triangle polynomial with periodic boundary conditions by Fourier spectral method,and show the existence and uniqueness of discrete solution,and give the convergence analysis.For Dirichlet boundary value problem of the Possion equation,the numerical solution is obtained by the Chebyshev spectral method and the error estimation is derived.Two classes of boundary value problems are verified by numerical examples.