Description
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.
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