  We present a formulation of special relativistic, dissipative hydrodynamics
(SRDHD) derived from the well-established M\"uller- Israel-Stewart (MIS)
formalism using an expansion in deviations from ideal behaviour. By re-summing
the non-ideal terms, our approach extends the Euler equations of motion for an
ideal fluid through a series of additional source terms that capture the
effects of bulk viscosity, shear viscosity and heat flux. For efficiency these
additional terms are built from purely spatial derivatives of the primitive
fluid variables. The series expansion is parametrized by the dissipation
strength and timescale coefficients, and is therefore rapidly convergent near
the ideal limit. We show, using numerical simulations, that our model
reproduces the dissipative fluid behaviour of other formulations. As our
formulation is designed to avoid the numerical stiffness issues that arise in
the traditional MIS formalism for fast relaxation timescales, it is roughly an
order of magnitude faster than standard methods near the ideal limit.
