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 Num. Meth. Prog., 2013, Volume 14, Issue 2, Pages 254–261 (Mi vmp111)

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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.

Full text: PDF file (177 kB)
UDC: 519.622

Citation: E. A. Novikov, “An integration algorithm using the methods of Rosenbrock and Ceschino”, Num. Meth. Prog., 14:2 (2013), 254–261

Citation in format AMSBIB
\Bibitem{Nov13} \by E.~A.~Novikov \paper An integration algorithm using the methods of Rosenbrock and Ceschino \jour Num. Meth. Prog. \yr 2013 \vol 14 \issue 2 \pages 254--261 \mathnet{http://mi.mathnet.ru/vmp111}