An inequality for the stability control of Ceschino's scheme of second order of accuracy is constructed. Based on the stages of this method, a numerical formula of order one is developed whose stability interval is extended to 32. On the basis of the L-stable Rosenbrock scheme and the numerical Ceschino's formula, an algorithm of alternating structure in which an efficient numerical formula is chosen at every step according to a stability criterion is proposed. The algorithm is intended for solving stiff and nonstiff problems. Numerical results confirm the efficiency of this algorithm.

Keywords: stiff problems, Ceschino's scheme, Rosenbrock's method, accuracy and stability control

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