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VariationalBound—Wolfram Documentation

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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.

Eigenvalue problem for a fourth-order ordinary differential equation:

The solution fits the equation well in this case:

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