Вычислительные методы и приложения

An integration algorithm using the methods of Rosenbrock and Ceschino

E. A. Novikov

Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk

Abstract: 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.

UDC: 519.622

Received: 14.04.2013