[R] Shooting methods in R?

[Paul Smith]

Dear All,

I would like to solve numerically the following minimization problem,
by discretization. (I already know the analytical solution, but my
goal now is to solve the problem numerically.) Someone told me that I
should look for "shooting methods". Does R implement "shooting
methods"? I have already searched the R site with the keywords
"shooting methods", but have got nothing.

PROBLEM: Find u(t) that minimizes

(1/2) * integral{from 0 to 1} (u(t))^2 dt

subject to

dx1 / dt = x2(t), x1(0) = x1(1) = 0,

dx2 / dt = u(t), x2(0) = 1, x2(1) = 0.

Paul