  Understanding grain-surface processes is crucial to interpreting the
chemistry of the ISM. However, accurate surface chemistry models are
computationally expensive and are difficult to integrate with gas-phase
simulations. A new modified-rate method for solving grain-surface chemical
systems is presented. Its purpose is accurately to model highly complex systems
that can otherwise only be treated using the sometimes inadequate rate-equation
approach. In contrast to previous rate-modification techniques, the functional
form of the surface production rates was modified, and not simply the rate
coefficient. This form is appropriate to the extreme "small-grain" limit, and
can be verified using an analytical master-equation approach. Various further
modifications were made to this basic form, to account for competition between
processes, to improve estimates of surface occupation probabilities, and to
allow a switch-over to the normal rate equations where these are applicable.
The new method was tested against systems solved previously using exact
techniques. Even the simplest method is quite accurate, and a great improvement
over rate equations. Further modifications allow the master-equation results to
be reproduced exactly for the methanol-producing system, within computational
accuracy. Small discrepancies arise when non-zero activation energies are
assumed for the methanol system, which result from complex reaction-competition
processes that cannot be resolved easily without using exact methods.
Inaccuracies in computed abundances are never greater than a few tens of
percent, and typically of the order of one percent, in the most complex systems
tested. Implementation of the method in simple networks, including
hydrogen-only systems, is trivial, whilst the results are highly accurate.
