I have been working on a problem which requires the use of Energy Methods which is based on the variational principles. I am finding it hard to replicate my formulated equations in Mathematica.
How can I find the variation of any parameter using the variational operator in Mathematica? I have been trying the following function with 'u' being the dependent variable.
𝛿F(x,u) means the variation in the function with respect to the dependent variable. If F(x,u) can be given as:
F(x,u)= f(x)+x^2*u(x)-2u du/dx + 2x*Sin u
How can I find the first and second variation of this function w.r.t the dependent variable?