VariationalBound


finds values of the parameters a, b, ... of a trial function that extremize the functional , where the integrand f is a function of u, its derivatives, and x.


finds values of the parameters of a trial function of two or more variables.


finds values of the parameters that extremize the ratio , where the integrands f and g are functions of u, its derivatives, and x.

DetailsDetails

  • To use , you first need to load the Variational Methods Package using Needs["VariationalMethods`"].
  • returns the extremal value of the functional as well as the optimal parameter values.
  • By default, the parameters a, b, ... may range over the interval to . A parameter specification of can be used to restrict the range to the interval to .

ExamplesExamplesopen allclose all

Basic Examples (1)Basic Examples (1)

In[1]:=
Click for copyable input

Eigenvalue problem for a fourth-order ordinary differential equation:

In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=

The solution fits the equation well in this case:

In[4]:=
Click for copyable input
Out[4]=
In[5]:=
Click for copyable input
Out[5]=
In[6]:=
Click for copyable input
New to Mathematica? Find your learning path »
Have a question? Ask support »