NVariationalBound


numerically searches for values of the parameters a, b, ... 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.

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.
  • 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 .

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

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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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