One-stage Rosenbrock method with complex coefficients and automatic time step evaluation

Well-known one-stage Rosenbrock scheme with complex coefficients is generalized to the case which allows to make a simple estimation of the truncation error. New version of such a scheme preserves all properties of the old one (such as $A$-stability and $L$-decrementation) and makes possible to choose step of integration automatically with the use of correction procedure.
Testing of strategy of time step evaluation as well as of new method has been done with the use of well known and original nonlinear differential equations and systems of equations include nonlinear equation of the heat conduction.