This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 VARIATIONAL METHODS PACKAGE SYMBOL

# NVariationalBound

 numerically searches for values of the parameters of a trial function , starting from , that extremize the functional , where the integrand f is a function of u, its derivatives, and x. searches for values of the parameters of a trial function of two or more variables. searches for values of the parameters that extremize the ratio , where the integrands f and g are functions of u, its derivatives, and x.
• returns the extremal value of the functional as well as the optimal parameter values.
• uses FindMinimum to search for values of the parameters that extremize the functional.
• A parameter specification of searches for an extremum using and as the first two values of a, avoiding the use of derivatives.
• A parameter specification of searches for an extremum, stopping the search if a ever gets outside the range to .
Eigenvalue problem for a third-order ordinary differential equation:
The solution fits the equation well in this case:
Needs["VariationalMethods`"]
Eigenvalue problem for a third-order ordinary differential equation:
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The solution fits the equation well in this case:
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