DIFFERENCE EQUATION
\dˈɪfɹəns ɪkwˈe͡ɪʒən], \dˈɪfɹəns ɪkwˈeɪʒən], \d_ˈɪ_f_ɹ_ə_n_s ɪ_k_w_ˈeɪ_ʒ_ə_n]\
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A relation between consecutive elements of asequence. The first difference isD u(n) = u(n+1)  u(n)where u(n) is the nth element of sequence u. The seconddifference isD2 u(n) = D (D u(n))= (u(n+2)  u(n+1))  (u(n+1)  u(n))= u(n+2)  2u(n+1) + u(n)And so on. A recurrence relation such asu(n+2) + a u(n+1) + b u(n) = 0can be converted to a difference equation (in this case, asecond order linear difference equation):D2 u(n) + p D u(n) + q u(n) = 0and vice versa. a, b, p, q are constants.
By Denis Howe
Word of the day
hydrophyllaceae
 perennial woodland herbs waterleaf plant family of the order Solanales, subclass Asteridae, class Magnoliopsida. They have alternate leaves, regular flowers with fivelobed corollas (united petals), and a one or twocelled ovary.