Previous: Numerical Theory Up: Numerical Theory Next: Taylor sequences

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.