Truncation error
Error introduced by cutting off an expansion or replacing a continuous object with a discrete one.
Definition
Truncation error appears when a Taylor series, interpolation or quadrature is stopped after finitely many terms. It is the main source of the powers in differentiation, integration and ODEs.
How it is used
Reducing lowers truncation error, but can increase rounding error; this is why finite-difference formulas have a practical optimal step.