In this paper we continue to develop the method on non-uniform grids for solving a boundary problem for elliptic equation in a semistrip. | Trần Đình Hùng Tạp chí KHOA HỌC & CÔNG NGHỆ 181(05): 55 - 59 METHOD OF INFINITE SYSTEM OF EQUATIONS ON NON-UNIFORM GRIDS FOR SOLVING A BOUNDARY PROBLEM FOR ELLIPTIC EQUATION IN A SEMISTRIP Tran Dinh Hung* University of Education - TNU ABSTRACT For solving boundary value problems in unbounded domains, one usually restricts them to bounded domains and find ways to set appropriate conditions on artificial boundaries or use quasiuniform grid that maps unbounded domains to bounded ones. Differently from the above methods we approach to problems in unbounded domains by infinite systems of equations. Some initial results of this method are obtained for several 1D problems. Recently, we have developed the method for an elliptic problem in a semistrip. Using the idea of Polozhii in the method of summary representations we transform infinite system of three-point vector equations to infinite systems of three-point scalar equations and show how to obtain an approximate solution with a given accuracy. In this paper we continue to develop the method on non-uniform grids for solving a boundary problem for elliptic equation in a semistrip. Key word: unbounded domain; elliptic equation; infinite system; method of summary representation; non-uniform grid INTRODUCTION* A number of mechanical as well as physical problems are posed in infinite (or unbounded) domains. In order to solve these problems, many authors often limit themselves to deal with the problem in a finite domain and make effort to use available efficient methods for finding exact or approximate solution in the restricted domain. But there are some questions which arise: how large size of restricted domain is adequate and how to set conditions on artificial boundary to achieve approximate solution with good accuracy? Mathematicans often try to define appropriate conditions on the boundary. These boundary conditions are called artificial or absorbing boundary conditions (ABCs) ([1], [9]). It is important notice .
