Summation by parts for discrete variables is the equivalent of integration by parts for continuous variables
![Delta^(-1)[v(x)Deltau(x)]=u(x)v(x)-Delta^(-1)[Eu(x)Deltav(x)],](/images/equations/SummationbyParts/NumberedEquation1.svg) |
(1)
|
or
![sum[v(x)Deltau(x)]=u(x)v(x)-sum[u(x+h)Deltav(x)],](/images/equations/SummationbyParts/NumberedEquation2.svg) |
(2)
|
where 
is the indefinite summation operator and the 
-operator is defined by
 |
(3)
|
where 
is any constant.
Summation by Parts
See also
Integration by PartsExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Summation by Parts." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SummationbyParts.html