VARIATIONAL METHODS PACKAGE SYMBOL

# 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)

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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