|MATLAB Function Reference|
If the matrix
U is regarded as a function evaluated at the point on a square grid, then
4*del2(U) is a finite difference approximation of Laplace's differential operator applied to , that is:
in the interior. On the edges, the same formula is applied to a cubic extrapolation.
For functions of more variables ,
del2(U) is an approximation,
where is the number of variables in .
L = del2(U)
U is a rectangular array is a discrete approximation of
L is the same size as
U with each element equal to the difference between an element of
U and the average of its four neighbors.
-L = del2(U)
U is an multidimensional array, returns an approximation of
L = del2(U,h)
H is a scalar uses
H as the spacing between points in each direction (
h=1 by default).
L = del2(U,hx,hy)
U is a rectangular array, uses the spacing specified by
hx is a scalar, it gives the spacing between points in the x-direction. If
hx is a vector, it must be of length
size(u,2) and specifies the x-coordinates of the points. Similarly, if
hy is a scalar, it gives the spacing between points in the y-direction. If
hy is a vector, it must be of length
size(u,1) and specifies the y-coordinates of the points.
L = del2(U,hx,hy,hz,...)
U is multidimensional uses the spacing given by
For this function,
4*del2(U) is also