METHOD OF INFINITE SYSTEM OF EQUATIONS ON NON-UNIFORM GRIDS FOR SOLVING A BOUNDARY PROBLEM FOR ELLIPTIC EQUATION IN A SEMISTRIP

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 quasi-uniform 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.