Finite Difference Methods For High-order Wave Equations And Sea Water Intrusion Models

The contents of this dissertation are divided into two chapters.Chapter one studied the finite difference methods of a class of high-order wave equations ?Section one considered the equation's two-order implicit schemes, By using the energy method, the priori estimations of convergence and stability of the difference scheme are proved, some numerical results are presented ?With the applications of variable replacement method , section two considered the equation's C-N schemes; the existence and the uniqueness of the difference solution are proved ; by using the energy method, the second-order convergence and unconditional stability of the schemes are proved; by using the extrapolation technique, the linearized scheme are devised , some numerical results are presented.Chapter two studied a block-centered finite difference method combined with char-acteristics for the numerical simulation of sea water intrusion models. The mathemat-ical models of sea water intrusion can be described by a system of nonlinear par-tial differential equations. One is fluid equation for the pressure, and the other one is advection-dispersion equation in form for the saltwater concentration. The block-centered finite difference schemes are applied to approximate the pressure equations, while the characteristic difference schemes based on fully quadratic rectangular inter-polation are applied to approximate the saltwater concentration equations. By using the priori estimation theory and techniques, the optimal order estimates in L2-norm are derived for the error in the approximate solution.