  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. In opposite to our previous
paper, the fourth stage is explicit. So, the constructed method also has a good
stability properties because of L-stability of the intermediate numerical
formulas in the fourth stage, but has a lower computational costs per step.
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.
