Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Novikov E. A. Algorithm Variable Order, Step and the Configuration Variables for Solving Stiff Problems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 3, pp. 35-43. DOI: 10.18500/1816-9791-2013-13-3-35-43

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Algorithm Variable Order, Step and the Configuration Variables for Solving Stiff Problems

Novikov Evgenii Aleksandrovich, Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences

An inequality for stability control of a Ceschino’s scheme of second order of accuracy is constructed. A numerical formula of order one is developed that is based on the stages of the this method and its stability interval is extended to 32. On a base of L-stable (2,1)-scheme and a numerical Ceschino’s formula, an algorithm of alternating structure, in which an efficient numerical formula is chosen on an every step by a stability criterion, is constructed. The algorithm is intended for solving stiff and non-stiff problems. There are shown results of calculations, confirming efficiency of this algorithm.

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