Singular perturbations for difference equations
Hsiao, George S.
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This paper discusses singular perturbations for second-order linear difference equations with a small parameter. It is found that there exhibits boundary layer behavior for the two-point boundary-value problem as well as for the final-value problem, but not for the initial-value problem. In contrast to problems for differential equations, a boundary layer exists only at the right end point. By virtue of a stretching transformation, a formal procedure is developed for treating such problems, and the justification of this procedure is established through a discrete maximum principle.
The article of record as published may be found at https://doi.org/10.1216/RMJ-1976-6-4-561
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