"An integration algorithm using the methods of Rosenbrock and Ceschino"
Novikov E.A.

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

Novikov E.A., e-mail: novikov@icm.krasn.ru – Institute of Computational Modelling, Siberian Branch of Russian Academy of Sciences; Akademgorodok, Krasnoyarsk, 660036, Russia