ABSTRACT 
In this article, we analyze a recentlypresented scheme for singularlyperturbed sys
tems of balance laws, the socalled Reference Solution Implicit Explicit scheme. RSIMEX scheme’s
bottomline is to use the Taylor expansion of the flux function and the source term around a reference
solution (typically the asymptotic limit or an equilibrium solution) to decompose the flux and the
source into stiff and nonstiff parts so that the resulting IMEX scheme is Asymptotic Preserving
(AP) w.r.t. the singular parameter ε as ε → 0. After a brief introduction to the scheme, we prove the
asymptotic consistency, asymptotic l 2 stability, solvability and wellbalancing of the scheme for the
case of the onedimensional shallow water equations and with two reference solutions (the lake at rest
and the zeroFroude limit). Thus, the scheme is AP and can be used for flows with various Froude
numbers. Finally we will test the scheme numerically for several test cases to show the quality of
the solutions and confirm the analysis.
