  In this paper we construct a third order method for solving additively split
autonomous stiff systems of ordinary differential equations. The constructed
additive method is L-stable with respect to the implicit part and allows to use
an arbitrary approximation of the Jacobian matrix. Automatic stepsize selection
based on local error and stability control are performed. The estimations for
error and stability control have been obtained without significant additional
computational costs. Numerical experiments show reliability and efficiency of
the implemented integration algorithm.
