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del2 | Examples See Also |
L = del2(U) L = del2(U,h) L = del2(U,hx,hy) L = del2(U,hx,hy,hz,...)If the matrix
U
is regarded as a function u(x,y) evaluated at the point on a square grid, then 4
*del2(U)
is a finite difference approximation of Laplace's differential operator applied to u, that is:del2(U)
is an approximation,L = del2(U)
where 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)
when U
is an multidimensional array, returns an approximation of
where N is ndims(u)
.
L = del2(U,h)
where H
is a scalar uses H
as the spacing between points in each direction (h=1
by default).
L = del2(U,hx,hy)
when U
is a rectangular array, uses the spacing specified by hx
and hy
. If 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,...)
where U
is multidimensional uses the spacing given by hx
, hy
, hz
, ...
The function
has
For this function, 4
*del2(U)
is also 4.
[x,y] = meshgrid(-4:4,-3:3); U = x.*x+y.*y U = 25 18 13 10 9 10 13 18 25 20 13 8 5 4 5 8 13 20 17 10 5 2 1 2 5 10 17 16 9 4 1 0 1 4 9 16 17 10 5 2 1 2 5 10 17 20 13 8 5 4 5 8 13 20 25 18 13 10 9 10 13 18 25
V = 4*del2(U) V = 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
diff
Differences and approximate derivatives
gradient
Numerical gradient