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VariationalBound

VariationalBound[f, u[x], {x, x_min, x_max}, u_t, {a}, {b}, ...]
finds values of the parameters a, b, ... of a trial function u_t that extremize the functional

, where the integrand f is a function of u, its derivatives, and x.

VariationalBound[f, u[x, y, ...], {{x, x_min, x_max}, {y, y_min, y_max}, ...}, u_t, {a}, {b}, ...]
finds values of the parameters of a trial function of two or more variables.

VariationalBound[{f, g}, u[x], {x, x_min, x_max}, u_t, {a}, {b}, ...]
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 VariationalBound, you first need to load the Variational Methods Package using Needs["VariationalMethods`"].

VariationalBound 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 {a, a_min, a_max} can be used to restrict the range to the interval a_min to a_max.