3.12. Solve analytically 2du dx +xd2u dx2 = 0 on 1 < x < 5 such that u(1) = 4 and u(5) =

0 . Use the corresponding SDE to estimate u(2), u(3) and u(4) and their errors.

Compare. Say we use m= 100 realizations with a time step of h = 0.001 : discuss how the errors improve with increasing m and/or decreasing h.