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Equation needs to be combined with initial conditions in order to produce an initial value problem. A numerical technique can then be used to calculate the position and velocity vectors of each particle at the following time interval. Given the position/velocity at time , one can calculate the position/velocity at time with:
Determination of an appropriate step size for the integration is a complicated issue. Too small a step size will waste computer time, while too large a step size may miss important critical points in the function, resulting in an incorrect answer.
A way is needed to keep the step size just small enough so that the answer is within a specified tolerance, yet isn't wasteful. To do this a measure of how bad the answer is will be needed.