Numerical Methods For Two Classes Of Nonlinear Evolution Equations

This thesis is divided into three chapters, two practical classes of Nonlinear evolution equations are considered. Characteristic centered finite difference method and cubic finite volume method for these models are proposed, and the related numerical analysis are considered.In chapter 1, two mathematical models and numerical methods are presented.In chapter 2, we develop the characteristic centered difference method for a class of nonlinear evolution equation in the rectangular domain. Both the approximate solution and error estimate of u, u_t, (?)u/(?)x, (?)u_t/(?)x are obtained. The method we discussed and the characteristic difference method based on linear interpolation have same computational procedure, and for approximate solution it has the same error estimate as the characteristic difference method based on quadratic interpolation. Moreover, the gradients of u, u_t is super-convergent order error estimate. Numerical results confirm that the feasibility and efficiency of our methods.In chapter 3, we present the finite volume element method to solve the mathematical model of a class of nonlinear problem of groundwater. Piecewise cubic trial functions and piecewise linear test functions are used to finally obtain error estimate in L~2 norms. Numerical results confirm that the efficiency of our methods are presented.