laplacian
Laplacian of scalar function
Description
Examples
Compute Laplacian of Symbolic Expression
Compute the Laplacian of this symbolic expression. By default,
laplacian
computes the Laplacian of an expression with respect to a
vector of all variables found in that expression. The order of variables is defined by
symvar
.
syms x y t laplacian(1/x^3 + y^2 - log(t))
ans = 1/t^2 + 12/x^5 + 2
Compute Laplacian of Symbolic Function
Create this symbolic function:
syms x y z f(x, y, z) = 1/x + y^2 + z^3;
Compute the Laplacian of this function with respect to the vector [x, y,
z]
:
L = laplacian(f, [x y z])
L(x, y, z) = 6*z + 2/x^3 + 2
Input Arguments
More About
Tips
If
x
is a scalar,laplacian(f, x) = diff(f, 2, x)
.
Alternatives
The Laplacian of a scalar function or functional expression is the divergence of the gradient of that function or expression:
Therefore, you can compute the Laplacian using the divergence
and
gradient
functions:
syms f(x, y)
divergence(gradient(f(x, y)), [x y])
Version History
Introduced in R2012a
See Also
curl
| diff
| divergence
| gradient
| hessian
| jacobian
| potential
| vectorPotential