Campus Livre
functionalDerivative
Functional derivative (Euler-Lagrange expression) of a functional.
Category: Mathematics > Calculus
Syntax
D = functionalDerivative(f, y)Functional derivative of int(f) with respect to the function y(x).
Description
In the calculus of variations a minimizing function makes the functional derivative zero, which is the Euler-Lagrange equation. For the integrand y^2 + y'^2 the result is 2*y - 2*y'', and setting it to zero gives the differential equation y'' = y.
Input arguments
f- Integrand, built from
y(x)and its derivatives. y- Symbolic function
y(x).
Output arguments
D- Symbolic function giving
dF/dy - d/dx(dF/dy') + d^2/dx^2(dF/dy'') - ....
Example
Euler-Lagrange expression
syms y(x)
f = y^2 + diff(y, x)^2;
D = functionalDerivative(f, y)Output
D(x) = 2*y(x) - 2*diff(y(x), x, x)