Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

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 (2) 

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

Version History

  • 1.0.0 – 11 February 2019

Related Resources

License Information