Lab Exercises )
Recommended reading from Numerical Recipes ("NR"):
Ch. 16, 17, 19.
Exercise 1.
As an example of a boundary value problem, suppose you launch a
projectivile vertically upward from elevation y=0 m, and
hit reaches a an altitude of 10 m at a time t=1 second
after launch. Assuming a constant downward acceleration of
a=-9.8 m/s^2, solve for the trajectory at 500 enenly spaced
times between 0 and 1 s. Do this numerically and compare with
the simple analytical result.
Exercise 2.
A metallic rod of length 0.1 m and thermal diffusivity D=2.3e-5 m^2/s
(typical of steel) is at a uniform temperature of 20 C at time t =
0. One end of the rod (x=0) is fixed at that temp, and the other
(x=0.1 m) is attached to a heat bath of T=100 C (Dirichlet boundary
conditions). Evolve the temperature in time until steady-state heat
flow is approximately reached. Use a straight-u[ explicit FD method.
Be careful of the Courant condition!
Repeat for the case where the cooler end of the rod (x=0) is insulated.
Exercise 3.
Solve the case of the rod as above with Dirichlet boundary conditions,
but this time using the Crank-Nikolson scheme.