truncation error

The error from replacing an exact mathematical process (an infinite sum, a limit) with a finite number of steps.

Truncation error is the error introduced by approximating an exact mathematical procedure -- an infinite series, a derivative's limit definition, a continuous integral -- with a finite computation, independent of any round-off in the arithmetic used to carry it out.

Examples

Approximating $f'(x)$ by the difference quotient $\dfrac{f(x+h)-f(x)}{h}$ instead of taking the limit $h\to0$ leaves a truncation error, present even in exact, infinite-precision arithmetic.