The Segmented Adomian Algorithm For Boundary Value Problems Of Partial Differential Equations On A Triangular Domain

The Adomian decomposition method overcomes the dependence of small param-eters in the traditional perturbation method.And it has good convergence and com-putational property.For boundary value problems of ordinary differential equations,Adomian decomposition method is very effective.But,for initial-boundary value prob-lems of partial differential equations,the traditional Adomian decomposition method is based on partial boundary conditions,not all boundary conditions.Thus,it is d-ifficult to control the error of the approximate solution on the boundary.Therefor,based on the existing weighted segmented Adomian algorithm of a plane rectangular region,for the boundary value problems of second order partial differential equations on triangular domains are studied.The specific contents are:In chapter 1,the development history and present situation and problems in ap-plication of Adomian decomposition method are briefly summarized.And the research goal of this paper is introduced.In chapter 2,based on the existing weighted segmented Adomian decomposition method,combined Adomian decomposition method with segmented skill,a segmented Adomian algorithm for partial differential equations on a plane triangle domain is presented.In this algorithm,except for the boundary line y=y_minand x=x_min,two small segment boundaries on x_min?x?d,y_min?y?d.The resulting solution accurately satisfy all other boundary conditions.The algorithm is successfully applied to the recharge effect model and heterogeneous aquifer models of a groundwater flow region.In chapter 3,the segmented Adomian algorithm in Chapter 2 is improved,a further improved segmented Adomian algorithm is proposed.In the algorithm,the boundary error is controled to be smaller than any given positive number.For the generality of the algorithm,we give the convergence theorem.At the same time,the further improved segmented Adomian algorithm is applied to the recharge effect model and heterogeneous aquifer model of a triangular groundwater flow region.In chapter 4,the nonlinear groundwater flow model is studied by the further improved segmented Adomian algorithm..In chapter 5,the summary and prospects of this paper are given.