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A form of Rosenbrock-type methods optimal in terms of the number of non-zero parameters and computational costs per step is considered. A technique of obtaining (m , k) -methods from some well-known Rosenbrock-type methods is justified. Formulas for transforming the parameters of (m , k) -schemes and for obtaining a stability function are given for two canonical representations of the schemes. An L -stable (3 , 2) -method of order 3 is proposed, which requires two evaluations of the function: one evaluation of the Jacobian matrix and one L U -decomposition per step. A variable step size integration algorithm based on the (3 , 2) -method is formulated. It provides a numerical solution for both explicit and implicit systems of ODEs. Numerical results are presented to show the efficiency of the new algorithm. [ABSTRACT FROM AUTHOR]