The following system has been used to study chemicals that are active in the atmosphere ozone depletion cycle [14, pp 317]. It involves the rapid formation of chlorine atoms from oxygen and hydrogen atoms and molecular chlorine:
There is a wide range of time constants in this problem that is typical of stiff ODEs. The numerical stability of most methods will be limited by and relative to the method's step size. Using the labeling
we arrive at the following set of ODE's:
For the initial conditions,
tabulate the solution at using both the Adams method (VODE with MF=10) and the BDF method (VODE with MF=22, internally generated Jacobian). Obtain the elapsed time for each solution. This problem would be classified as mildly stiff and you should notice a considerable difference in the elapsed solution times. For error tolerances use, ITOL=1, RTOL=, and ATOL=.