Numerical Approximation Of Parabolic Integro-Differential Equations And Initial-Value Problems Of Purely Longtudinal Motion Of A Homogeneous Bar

In this paper , we consider numerical approximation for the initial-boundary value problems of parabolic integro-differential equations and purely longtudinal motion equations of a homogeneous bar. obtain the error estimates of the discrete schemes for the two kinds of problems.In Chapter one and Chapter two , we consider the expanded mixed finite element methods and mixed covolume method for the initial-boundary value problems of Linear second-order integro-differential equation of parabolic type. The expanded mixed finite element methods is a extend of the mixed finiteelement methods. In this expands mixed formulation three variable are explixitly treated:the scalar unknwon, its gradient and its flux. We develop the semi-discrete schemes and obtain optimal-order error estimates in the L2-norm.In Chapter two, Using the lowest order Raviart-Thomas mixed element space on rectangles , we present a mixed covolume method for the initial-boundary value problems of linear second-order integro-differential equation of parabolic type.Weprove the first order optimal L2-norms error estimates of the solution of this mixed covolume scheme.In Chapter three, we consider the generalized difference methods for the following initial-value problems of purely longtudinal motion of a homogeneous bar.In this chapter,we give the error analysis of the solution of the generalized difference scheme and get optimal error estimates for the semi-discrete scheme .