BVP: Optimization

Consider the BVP example again:

If we knew the value of y'(0)  at the initial point then this becomes an initial value problem and we know how to solve it from the previous pages

One way of solving the problem is to iterate to the solution the following way

  1. Guess y'(0)
  2. Solve the initial value problem
  3. Note the value of y(3). Unless you are very lucky it will not not be 0.5.  This suggests that the initial guess needs to be modified .  Make another guess and do step 2 again.  These iterations (or the loop) will be carried out until  y(3) = 0.5


Guessing at random will take forever to hit the solution.  Optimization techniques are designed to iterate by guessing smartly in each iteration (except the first) so that the solution can be obtained rapidly