Cite this article as:

Novikov E. A. Variable Order and Step Algorithm Based on a Stages of Runge – Kutta Method of Third Order of Accuracy. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2011, vol. 11, iss. 3, pp. 46-53. DOI: https://doi.org/10.18500/1816-9791-2011-11-3-1-46-53

Language: 
Russian
Heading: 
Mathematics
UDC: 
519.622

Variable Order and Step Algorithm Based on a Stages of Runge – Kutta Method of Third Order of Accuracy

Authors: 
Novikov Evgenii Aleksandrovich, Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Russia, 660036, Krasnoyarsk, Akademgorodok , novikov@icm.krasn.ru
Abstract: 

An inequality for the stability control of 3-stage Runge – Kutta method of 3th order of accuracy is obtained. Method of first order with expanded stability domain is constructed. Algorithm of variable order is formulated. The results of stiff system computations are provided, which confirm an increase in efficiency for the variable order method as compared to a calculation with fixed scheme.

Key words: 
stiff problems, explicit method, stability and accuracy control, variable order.
DOI: 
https://doi.org/10.18500/1816-9791-2011-11-3-1-46-53
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