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Find the values of parameters of a trial function that extremize a functional
ResourceFunction["VariationalBound"][f,u[x],{x,xmin,xmax},ut,{a},{b},…] finds values of the parameters a,b,… of a trial function ut that extremize the functional , where the integrand f is a function of u, its derivatives and x. | |
ResourceFunction["VariationalBound"][f,u[x,y,…],{{x,xmin,xmax},{y,ymin,ymax},…},ut,{a},{b},…] finds values of the parameters of a trial function of two or more variables. | |
ResourceFunction["VariationalBound"][{f,g},u[x],{x,xmin,xmax},ut,{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:
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The solution fits the equation well in this case:
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