 Parasitic amplification root

An amplification root of a multistep method is parasitic when it represents an additional numerical mode rather than the principal mode approximating the exact differential-equation flow. For a consistent method the principal root starts at one as the step tends to zero, while other roots can start elsewhere. A simple parasitic root on the unit circle is compatible with zero-stability, but its motion outside the circle for a negative test parameter can destroy absolute stability. Fixed-time convergence and all-time damping must be distinguished.