Wolfram Research

Function Repository Resource:

VariationalD

Source Notebook

Get the variational derivative of a functional

Contributed by: Wolfram Research

ResourceFunction["VariationalD"][f,u[x],x]

returns the variational derivative of the integral with respect to u[x], where the integrand f is a function of u, its derivatives and x.

ResourceFunction["VariationalD"][f,u[x,y,],{x,y,}]

returns the variational derivative of the multiple integral with respect to u[x,y,], where f is a function of u, its derivatives and the coordinates x,y,....

ResourceFunction["VariationalD"][f,{u[x,y,],v[x,y,],},{x,y,}]

gives a list of variational derivatives with respect to u,v,....

Examples

Basic Examples

Variational derivative for the arc length of a plane curve:

In[1]:=
ResourceFunction["VariationalD"][Sqrt[1 + y'[x]^2], y[x], x]
Out[1]=

Variational derivative for the Dirichlet integral in two variables:

In[2]:=
ResourceFunction["VariationalD"][D[u[x, y], x]^2 + D[u[x, y], y]^2, u[x, y], {x, y}]
Out[2]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

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