difference equation

[′dif·rəns i′kwā·zhən] (mathematics) An equation expressing a functional relationship of one or more independent variables, one or more functions dependent on these variables, and successive differences of these functions.

difference equation

A relation between consecutive elements of a sequence. Thefirst difference is

D u(n) = u(n+1) - u(n)

where u(n) is the nth element of sequence u. The seconddifference is

D2 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 as

u(n+2) + a u(n+1) + b u(n) = 0

can be converted to a difference equation (in this case, asecond order linear difference equation):

D2 u(n) + p D u(n) + q u(n) = 0

and vice versa. a, b, p, q are constants.

单词	difference equation
释义	difference equation difference equation [′dif·rəns i′kwā·zhən] (mathematics) An equation expressing a functional relationship of one or more independent variables, one or more functions dependent on these variables, and successive differences of these functions. difference equation A relation between consecutive elements of a sequence. Thefirst difference is D u(n) = u(n+1) - u(n) where u(n) is the nth element of sequence u. The seconddifference is D2 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 as u(n+2) + a u(n+1) + b u(n) = 0 can be converted to a difference equation (in this case, asecond order linear difference equation): D2 u(n) + p D u(n) + q u(n) = 0 and vice versa. a, b, p, q are constants.
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