meaning of difference equation
1. difference equation A relation between consecutive elements of a sequence. The first difference is D un = un+1 - un where un is the nth element of sequence u. The second difference is D2 un = D D un = un+2 - un+1 - un+1 - un = un+2 - 2un+1 + un And so on. A recurrence relation such as un+2 + a un+1 + b un = 0 can be converted to a difference equation in this case, a second order linear difference equation: D2 un + p D un + q un = 0 and vice versa. a, b, p, q are constants.
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