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We present a loosely coupled, non-iterative time-splitting scheme based on Robin–Robin coupling conditions. We apply a novel unified analysis for this scheme applied to both a parabolic/parabolic coupled system and a parabolic/hyperbolic coupled system. We show for both systems that the scheme is stable, and the error converges asO    (    Δ  t    T  +  log  (   1   Δ  t    )    )   ,    $\mathcal{O}\big({\Delta t} \sqrt{T +\log(\frac{1}{{\Delta t}})}\big),$   where  Δt  is the time step.

journal of numerical mathematics

Loosely coupled, non-iterative time-splitting scheme based on Robin–Robin coupling: Unified analysis for parabolic/parabolic and parabolic/hyperbolic problems