= Bounded solution of a second-order constant-coefficient recurrence
For a <linear recurrence relation> with two distinct <characteristic equation of a linear recurrence> roots $r_1,r_2$, the solution is $u_n=Ar_1^n+Br_2^n$. If $|r_1|<1<|r_2|$, boundedness for $n\to\infty$ forces $B=0$, and $u_0$ fixes $A$. This selects the decaying discrete mode in a <finite difference method> for a boundary problem on an unbounded interval. Roots on the unit circle require separate treatment; a repeated root there can contribute an unbounded factor $n$.
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