In order to select an adequate numerical method, some informations must be extract from the
input data. For example,
if the equations system is linear in the dependent variables, we can find the exact solution;
if the system is nonlinear, but it has a special form, it is possible to know the exact solution;
if we can identify two or more subsystems which are independent from each other then the system is separable. All the computations are faster if we work on this
subsystem rather then the full system. On the other hand, the computations on different subsystems can be made in concurrent processes, and if we dispose of a
local network and a software for intercommunication, we can distribute these computations on different workstation processors;
if the Jacobian matrix associated to the system function and evaluated to the initial value
is a sparse matrix, we can store only the nonzero values, and the same scheme we can apply to
each reevaluation of the Jacobian matrix;
in order to classify the problem as a nonstiff or a stiff one, we can use a formula for the
stiff ratio,
where J is the Jacobian matrix (d f/d y)(y0), s(J)={li | i=1, ... ,n} is the set of
J's eigenvalues, and e is the admitted error level (which must be controlled somehow by the user).
Therefore, we must find the biggest eigenvalue;
in order to estimate the computation time of an approximate solution we must estimate the time
of one evaluation of the right side of the ODE system.
