Hello,

I can't find the 9 point 2D laplacian operator in finite differences for
dx != dy. I have just found the one for dx=dy=h.

Can somebody tell me what it is ? (and maybe how to find it)

Thanks

On Jun 3, 5:57 pm, Nico <nicolas.au... at (no spam) free.fr> wrote:
Hello,

I can't find the 9 point 2D laplacian operator in finite differences for
dx != dy. I have just found the one for dx=dy=h.

Can somebody tell me what it is ? (and maybe how to find it)

Thanks

Taylor expansion is always helpful,

Write an ansats a11 u_{-dx,dy} + a12 u_{0,dy} + a13 u_{dx,dy} + ...
a21 u_{-dx,0} + a22 u_{0,0} + a23 u_{dx,0} + ...
a31 u_{-dx,-dy}+ a32 u_{0,-dy}+ a32 u_{dx,-dy}
= u_xx + u_yy + o(dx^p + dy^p)

Taylor expand the left hand side, with partial derivatives (include at
least 9 terms) and put equal to the corresponding coefficients in the
right hand side... (0 u:s, 0 u_x:s, ..., 1 u_xx, 1 u_yy, ...)

--
Henrik Holst, Sweden