Optimal schemes for stiff nonautonomous systems

Detailed investigation was performed for the next numerical methods of solving of stiff nonautonomous systems of ordinary differential equations: one- and two-staged schemes of Rosenbrock, Wanner and Novikov types and also one-staged schemes of these types with one complex coefficient. Theoretical properties of 13 schemes occured to be favourable. These schemes were checked with the test of shock wave type. Five schemes provide the best accuracy and robustness; they are recommended for programming codes.