Study Of Some Boundary Value Problems Of Second-Order Partial Differential Equations By Adomian Decomposition Method

With the development of the science,people gradually find that many practical problems are to be boundary value problems of nonlinear partial differential equation.So it has practical significance to study boundary value problems of partial differential equations.In this paper,based on the Adomian decomposition method to study boundary value problem of partial differential equations.The ADM is a decomposition method to solve the approximate solution of differential equation boundary value problems.It overcomes the reliance on small parameter of traditional perturbation method.However,there are many issues to be solved in the application of Adomian decomposition method to(initial)boundary value problems for partial differential equations.The specific contents of this paper are as follows:In chapter 1,the development history,current situation and problems in the applications of Adomian decomposition are briefly summarized,and the research objectives of this paper are introduced.In chapter 2,based on the Adomian decomposition method the boundary value problem of a wave equation in a rectangular region is studied,and its exact solution is obtained.Based on the Adomian decomposition method,the groundwater recharge effect model in the triangle region is studied.Its solution satisfying some boundary conditions are given.Based on the Adomian decomposition method,the viscous heating problem of planar couette flow is studied,and we found that for the same values of?,if the recursion formulae are different,their precisions of the approximate solutions are different,which indicates the flexibility of the Adomian decomposition method and the effectiveness for the boundary value problem of differential equations.The traditional Adomian decomposition method is only based on partial boundary conditions,not all.So,there is not guarantee that approximate solution satisfy all of boundary conditions.For this,in chapter 3,we proposed a algorithm for a boundary problem of partial equation on a triangular domain based on Adomian decompositionmethod.The solution obtained by the algorithm satisfy all of boundary conditions.By the algorithm,we solved the heterogeneous aquifer model of a triangular groundwater region and a boundary value problem of a nonlinear wave equation.