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