If is known, can be calculated by evaluating the Taylor
series (1.1) with set to . Since the Taylor
series is an infinite sum, you have to truncate the series after
terms, so you introduce an error that scales with the magnitude of the
'th term. This error is called the *local truncation
error*. It scales with .

Successive application of the series on the obtained results, gives a sequence of numbers . If is considered a time step, this simple scheme allows you to approximate any continuous function or - as we use to call it - simulation of the variable described by that function.

The accumulation of the local truncation errors in such an
approximation or simulation is called the *global truncation
error*. To obtain more accuracy in the results, it is obvious that
should be made smaller. This however results in more steps needed
for the same simulated time. If you divide by two for example,
the number of steps needed to obtain the same simulated time is
multiplied by two with more accumulation of local error as a result.
In general the global truncation error is always at most one order of
magnitude larger than the local truncation error.