MATLAB Function Reference |

**Syntax**

**Definition**

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 .

**Description**

```
L = del2(U)
```

where `U`

is a rectangular array is a discrete approximation of

The matrix `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

```
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`

, ...

**Examples**

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

**See Also**

deconv | delaunay |