Unified approach to spurious solutions introduced by time discretisation. Part I. Basic theory
The asymptotic states of numerical methods for initial value problems are examined. In particular, spurious steady solutions, solutions with period 2 in the timestep, and spurious invariant curves are studied. A numerical method is considered as a dynamical system parameterised by the timestep h. It is shown that the three-kinds of spurious solutions can bifurcate from genuine steady solutions of
