On 5 Aug 2014, at 0:54, James Crist wrote:
It's highly unlikely you'd create an Indexed that did an operation
with a
Matrix, but a Matrix with Indexed elements, yes as this is what would
happen in a finite difference model.
Would you write it as Matrix([indexed_thing, indexed_thing_2, ...]),
or
just use the indexed object support for the outer Matrix as is already
shown in the docs?
It would be something like Matrix([A[i+1], -2*A[i], A[i-1], ...]). At
least for the linear case. It would be more complex for the non-linear
case. This is just a simple case, but you can get differences in 4
dimensions (3 space and 1 time), that's why it's not just matrix
entries. But there is a mapping between them.
My course text for finite differences was, Numerical Solution of Partial
Differential Equations by G.D. Smith. It's probably in the university
library. It doesn't get into more than 2 dimensions (two space or 1
space and 1 time), but it covers the basics pretty well including their
use for the solution of parabolic, hyperbolic, and elliptical PDEs.
Finite differences aren't used as much anymore since finite volume and
finite element methods have been developed, but they're easy to
implement and work for pretty much any type of problem. Maple's
numerical PDE solver uses finite differences internally last I checked.
Cheers,
Tim.
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