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# Questions tagged [variational-calculus]

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### How to solve calculus of variations problems numerically?

For example, how to solve the well-known isoperimetric problem (i.e., to enclose the largest area with a fixed-length curve)? We can simplify things a bit and fix the two ends of the curve at $[a,0]$,...
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I am confused. I read an introduction to finite element method where it was derived for the poisson equation: $$-\Delta u + cu = f,\qquad, u = g_0 \text{ on Dirichlet boundaries},\qquad\partial_n u ... 0answers 97 views ### functional second derivative I'm trying to build a numerical solution for a parameter estimation problem of reaction-diffusion equation, using the adjoint method. To summarize it, I'm trying to minimize the function$$ G=\frac{...
Calculus of variations problems are generally cast in in the following simple form: find $u(t)$ that satisfies some boundary conditions and minimises  F[u] = \int_{t=0}^{t=t_f} f(u(t),u'(t),t) dt. \$...