Abstract
An ad hoc method to solve boundary value problems which are posed on infinite intervals is to reduce the infinite interval to a finite but large one and to impose additional boundary conditions at the far end. These boundary conditions should be posed in a way so that they express the asymptotic behavior of the actual solution well. In this paper a theory is derived which defines classes of appropriate additional boundary conditions. Appropriate is to be understood in the sense that the solutions of the approximate problems converge to the actual solution of the 'infinite' problem as the length of the finite interval tends to infinity. Moreover, boundary conditions which produce convergence with the largest expectable order are devised.