Re: Irregularly gridded Discrete Laplacian Operator

[Jordi Gutiérrez Hermoso]

On 18/07/07, David Bateman <address@hidden> wrote:
> The definition for the interior points along an axis of 1D problem for
> the octave-forge version of del2 can be written as
>
> D (2:end-1) =  (M(3:end) - 2 * M(2:end  - 1) + M(1:end -2)) ./
> (dx(1:end-1) .* dx(2:end)) ./ 2

This is just the common O(h^2) approximation to the second derivative,
(f(x+h) - 2f(x) - f(x-h) )/h^2 where it looks like they took the h's
slightly spaced apart in order to account for small differences in h?
Taking a square root in the denominator here would make no sense; the
denominator has to be a square in h, not linear.

> whereas the equivalent in Matlab appears to be
>
> D(2:end-1) = ((M(3:end) - M(2:end-1)) ./  dx(2:end) + (M(1:end-2) -
> M(2:end-1)) ./ dx(1:end-1)) ./ (dx(1:end-1) + dx(2:end))

I don't understand this one either. Looks like some sort of averaging
like you said.

- Jordi G. H.