  In this paper we present a technique for constructing robust solvers for
stiff algebraic source terms, such as those typically used for modelling
relaxation processes in hyperbolic systems of partial differential equations
describing two-phase flows, namely models of the Baer-Nunziato family. The
method is based on an exponential integrator which employs an approximate
linearised source term operator that is constructed in such a way that one can
compute solutions to the linearised equations avoiding any delicate matrix
inversion operations.
