Numerical integration techniques
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## Numerical integration techniques

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:

where

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.

*mcr@ccs.carleton.ca*