Truncation error in SPH

Statement of the problem
What is the error in the approximation
First SPHERIC Workshop, Rome, 2006
a
( )
∂A
∂W x − x
≅ −∑ A( x )
Δx
∂x ∂x
b a
b b
x = x b
b
a
b
( x )
∇A ≅ − A ∇ W V
x= x
∑
b b a b
(nD)
(1D)