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Multirate behavior of ordinary differential equations (ODEs) anddifferential-algebraic equations (DAEs) is characterized by widely separatedtime constants in different components of the solution or different additiveterms of the right-hand side. Here, classical multirate schemes are dedicatedsolvers, which apply (e.g.) micro and macro steps to resolve fast and slowchanges in a transient simulation accordingly. The use of extrapolation andinterpolation 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 schemesfor both ODEs and DAEs of index one, which are based on the fully-decoupledapproach, the slowest-first and the fastest-first approach. The convergencetheory is based on linking these schemes to multirate dynamic iterationschemes, i.e., dynamic iteration schemes without further iterations. This linkdefines naturally stability conditions for the DAE case.

Inter/extrapolation-based multirate schemes -- a dynamic-iteration perspective