Consider the differential equation for the displacement u of a bar of length L hanging under its own weight (figure): . (1) The boundary conditions are: u(0) = 0, u0(L) = 0. (2) Solve the above differential equation using the second-order finite-difference method. Compare your numerical results with the theoretical result for different mesh-sizes, and in doing so, show the convergence of the numerical results with mesh-size. Also determine the corresponding convergence rate. 1
