Numerical Methods Of Several Kinds Of Evolution Equations

In this paper,some numerical approximation methods are proposed and analyzed for several kinds of evolution equations.In chapter one and two,we consider the finite element numerical approximation for the initial boundary value problem for the next two evolution equations. (1) Linear Quasi-parabolic Integro-differential Equation(2)Linear Quasi-hyperbolic Integro-differential EquationWe obtain Lp-optimal and W1,p- optimal estimats under the certain condition(2 ≤ p < ∞).In chapter three,Generalized Difference Methods(GDM) for one-dimensional linear quasi-parabolic integro-differential equations.The new initial values are given in the generalized difference scheme ,so we obtain optimal error estimates in Lp and W1,p(2 ≤ p ≤ ∞) as well as some superconvergence estimates in W1,9(2 ≤p≤ ∞) between the GDM solution and the generalized Sobolev-Volterra projection of the exact solution.