Abstract
The article presents generalization of the well-known one-stage Rosenbrock scheme with complex coefficients. The obtained method preserves all the advantages of its previous version (A stability and L damping), provides a simple estimation of the local error and facilitates the easy selection and correction of the integration step. The strategy of the selection of the step and the new method is tested both on the basis of known and original nonlinear equations and sets of nonlinear equations, as well as of the nonlinear equation of thermal conductivity.
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