Study On Numerical Methods For Several Classes Of Partial Differential Equations With Spatial-temporal Mixed Derivatives

This master thesis is composed of five parts. The first chapter briefly in-troduces the preliminary knowledge, discussed in the text Sobolev the practical application of equations in Mathematical Physics.In section2,we introduce Ex-panded Mixed Covolume Method,and how to use the Semi-discrete expanded mixed finite volume element method to solve Sobolev Equation.Mainly introduces the advantages of the introduction of the three inter-mediate variables, mixed finite volume element of the development process, and use of the advantages of this method in solving this kind of equation. In section3.two conservative finite difference schemes for the numerical so-lution of the initial-boundary value problem of general Rosenau-KdV-RLW equation are proposed,the first one is a two-level nonlinear Crank-Nicolson difference scheme and the second one is a three-level linear implicit difference scheme.We first verify that the two difference schemes simulate two conserva-tive quantities of the problem very well.At the same time, existences of the two numerical solutions are proved by the Browder fixed point theorem, con-vergences, unconditional stabilities as well as uniqueness of the solutions are also derived using energy method. Finish, numerical examples are carried out to verify the correction of the theory analysis.