Several Numerical Simulation Of Some Kinds Of Evolution Equations

In this paper, we consider numerical simulation of some kinds of evolution equations. In chapter one,we consider the Generalized Galerkin Method numerical simulationfor the two-point boundary problemand parabolic problemin one dimension. We obtain L2-optimal and H1-optimal estimates under the certain condition.In chapter two,we consider first order generalized difference scheme for linear Sobolev equation in one dimension.Lp and HW1,p-norm error estimates of the Ritz-Volterra projection u ?Vhu and H1-norm error estimate of ut ?(Vhu)t are made,so we obtain Lp and W1,p-norm error estimates of u-uh.In chapter three,we consider first order generalized difference scheme for linear Sobolev equation in two dimensions.Lp and W1,p-norm error estimates of the Ritz-Volterra projection u-Vhu and W1,p-norm super error estimate of uh-Vhu are made,so we obtain Lp and W1,p-norm error estimatesOf u-uh.