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

# 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.
• 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 .
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:
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The solution fits the equation well in this case:
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