Several Finite Difference Schemes For A Family Of Nonlinear PDES

Because many mathematical models of the physical phenomenon and process all can be denoted by the nonlinear partial differential equations. In many causes, it is very difficult to solve the exact solution of these nonlinear PDES. Therefore, the numerical method of the PDES plays an important role in the numerical analysis. In these recent dozens of years, its theory and method have great development. Moreover, the application of its is more and more extensive in every technology field.As a numerical discreatization method, for its easy operation and great agility character in the solving problem, the finite difference has gotten extensive application in the science research and computation. With the rapid development of the computer, how to get the fine and true numerical simulation has become an important task. Untill now, there are a lot of finite difference methods, but Taylor expandness method is very important in the finite difference methods as a classical and simply method. This paper has proposed by Taylor expandness method.The full text altogether divides into five chapters. In first chapter, we introduce the finite difference theory history, the present situation and provide the typical study method and main result with innovation. The second chapter, some readiness knowledge is given. The third, fourth and fifth chapters, three finite difference schemes were proposed. Convergence and stability of the difference solution were proved. The fourth and fifth chapers, numerical results demonstrate that the methods proposing are efficient and reliable.