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THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE
DOCUMENTATION CENTER
FOR THE LATEST INFORMATION.
DOCUMENTATION CENTER SEARCH
New to
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»
Variational Methods Package
>
VARIATIONAL METHODS PACKAGE SYMBOL
Variational Methods
Tutorials »
|
NVariationalBound
See Also »
|
Variational Methods Package
More About »
VariationalBound
finds values of the parameters
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
.
MORE INFORMATION
To use
, you first need to load the
Variational Methods Package
using
.
returns the extremal value of the functional as well as the optimal parameter values.
By default, the parameters
may range over the interval
to
. A parameter specification of
can be used to restrict the range to the interval
to
.
EXAMPLES
CLOSE ALL
Basic Examples
(1)
Eigenvalue problem for a fourth-order ordinary differential equation:
The solution fits the equation well in this case:
Needs["VariationalMethods`"]
Eigenvalue problem for a fourth-order ordinary differential equation:
In[2]:=
In[3]:=
Out[3]=
The solution fits the equation well in this case:
In[4]:=
Out[4]=
In[5]:=
Out[5]=
In[6]:=
SEE ALSO
NVariationalBound
TUTORIALS
Variational Methods
MORE ABOUT
Variational Methods Package