  Multirate behavior of ordinary differential equations (ODEs) and
differential-algebraic equations (DAEs) is characterized by widely separated
time constants in different components of the solution or different additive
terms of the right-hand side. Here, classical multirate schemes are dedicated
solvers, which apply (e.g.) micro and macro steps to resolve fast and slow
changes in a transient simulation accordingly. The use of extrapolation and
interpolation procedures is a genuine way for coupling the different parts,
which are defined on different time grids.
  This paper contains for the first time, to the best knowledge of the authors,
a complete convergence theory for inter/extrapolation-based multirate schemes
for both ODEs and DAEs of index one, which are based on the fully-decoupled
approach, the slowest-first and the fastest-first approach. The convergence
theory is based on linking these schemes to multirate dynamic iteration
schemes, i.e., dynamic iteration schemes without further iterations. This link
defines naturally stability conditions for the DAE case.
