AN EFFECTIVE NUMERICAL TECHNIQUE FOR SOLVING A SPECIAL-CLASS OF ORDINARY DIFFERENCE-EQUATIONS

We consider a system of ordinary difference equations with constant co efficients, which is defined on an infinite one-dimensional mesh. The right-hand side (RHS) of the system is compactly supported, therefore, the system appears to be homogeneous outside some finite mesh interva l. At infinity, we impose certain boundary conditions, e.g., condition s of boundedness or decay of the solution, so that the resulting bound ary-value problem is uniquely solvable and well posed. We also conside r a truncation of this infinite-domain problem to some finite mesh int erval that entirely contains the support of the RHS. We require that t he solution to this truncated problem, which is the one we are going t o actually calculate, coincides on the finite mesh interval where it i s defined with the corresponding fragment of the solution to the origi nal (infinite) problem. This requirement necessitates setting some spe cial boundary conditions at the ends of the aforementioned finite inte rval. In so doing, one should guarantee an exact transfer of boundary conditions from infinity through the (semi-infinite) intervals of homo geneity of the original system. It turns out that the desired boundary conditions at the ends of the finite interval can be naturally formul ated in terms of the eigen subspaces of the system operator. This, in turn, enables us to develop an effective numerical algorithm for solvi ng the system of ordinary difference equations on the finite mesh inte rval. This algorithm can be referred to as a version of the well-known successive substitution technique but without its final (''inverse'' or ''resolving'') stage. The special class of systems described in thi s paper appears to be most useful when constructing highly accurate ar tificial boundary conditions (ABCs) for the numerical treatment of pro blems initially formulated on unbounded domains. Therefore, an effecti ve numerical algorithm for solving such systems becomes an important i ssue.