Numerical Divergence
- To: mathgroup at smc.vnet.net
- Subject: [mg42909] Numerical Divergence
- From: Selwyn Hollis <selwynh at earthlink.net>
- Date: Sat, 2 Aug 2003 04:12:34 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I've made a couple of attempts at writing a function
NDiv[f_List, x:{_Symbol..}, h_Real][p:{_?NumericQ..}]
that computes a numerical approximation of div(f) at p, using central
differences with stepsize h. My (successful) attempts have used (1) Tr
and (2) MapIndexed, and neither is very fast. Since the divergence can
be computed symbolically as
Inner[D,f,x,Plus],
one would think that NDiv could be computed in an some analogous way
with Inner. However, my attempts have been unsuccessful.
Can any of you wizards help me out?
FYI: Here's the basic idea of my MapIndexed version:
NDiv[f_List, x:{_Symbol..}, h_Real][p:{_?NumericQ..}] :=
Module[{nPD, idm = IdentityMatrix[Length[p]]},
nPD[f_, {i_}] :=
((f/.Thread[x-> p+h*idm[[i]]]) - (f/.Thread[x->
p-h*idm[[i]]]))/(2*h);
Plus@@MapIndexed[nPD, f] ]
-----
Selwyn Hollis
http://www.math.armstrong.edu/faculty/hollis