Some Numerical Solutions Of Nonlinear Equations Time Behavior

Burgers equation possessing a global attractor is considered.First of all,we construct a semidiscrete finite difference scheme to Burgers equation with initial condition and Dirichret boundary conditions.The existence of global attractor is proved for the semidiscrete system firstly.Then in the autonomous system case,we obtain the stability of the semidiscrete finite difference scheme and the error estimate of the difference solution.Finally,the long-time stability and convergence of this finite difference scheme are also analysed in the nonautonomous system case.Then we construct a completely discrete finite difference scheme to Burgers equation.By using the same procedures as the discussion of the semisdiscrete system, we get some theories which are opposite to the theories of semidiscrete system in this discrete system.