Abstract
Boundary value problems for ordinary differential equations on infinite intervals are often solved by restricting the problem to a large but finite interval and imposing certain supplementary boundary conditions at the far end. The success of this procedure depends on the proper choice of these conditions. For a rather general class of problems we give a characterization of all possible supplementary boundary conditions which work, examine the rate of convergence of the solution of the “finite” problem to that of the original “infinite” problem as the interval length of the finite problem tends to infinity, and describe the supplementary boundary conditions for which this rate is optimal.
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