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The time required for ode to solve numerically a system of
ordinary differential equations depends on a great many factors.
A few of them are: number of equations, complexity of equations
(number of operators and nature of the operators), and number of
steps taken (a very complicated function of the difficulty of
solution, unless constant stepsizes are used). The most
effective way to gauge the time required for solution of a
system is to clock a short or imprecise run of the problem, and
reason as follows: the time required to take two steps is
roughly twice that required for one; and there is a relationship
between the number of steps required and the relative error
ceiling chosen. That relationship depends on the numerical
scheme being used, the difficulty of solution, and perhaps on
the magnitude of the error ceiling itself. A few carefully
planned short runs may be used to determine this relationship,
enabling a long but imprecise run to be us