Vasilyev E.I., Vasilyeva T.A., Kiseleva M.N. L-stability of multi-implicit methods of 8-th order for differential stiff systems

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http://dx.doi.org/10.15688/jvolsu1.2013.1.6

Vasilyev Evgeniy Ivanovich

Doctor of Physics and Mathematics, Professor, Department of Computer Science and Optimal Control, Volgograd State University
vasil-ei@vlink.ruThis email address is being protected from spambots. You need JavaScript enabled to view it.
Prospect Universitetskij, 100, 400062 Volgograd, Russian Federation

Vasilyeva Tatiana Anatolievna

Associate Professor, Department of Computer Science and Optimal Control,
Volgograd State University
tatiana_vas@mail.ruThis email address is being protected from spambots. You need JavaScript enabled to view it.
Prospect Universitetskij, 100, 400062 Volgograd, Russian Federation

Kiseleva Maria Nikolaevna
Postgraduate student, Department of Computer Science and Optimal Control,
Volgograd State University
fiou@volsu.ruThis email address is being protected from spambots. You need JavaScript enabled to view it.
Prospect Universitetskij, 100, 400062 Volgograd, Russian Federation

Abstract. The new set of absolutely stable difference schemes for a numerical
solution of ODEs stiff systems (1) is submitted.

At arbitrary (α, β) parameters last difference equation in (2) has 8-th order of ap-
proximating.
We found that the set of absolutely stable 3ISD-schemes includes two one parameter families: the set of the L-stable schemes and the set of the schemes of heightened accuracy for linear problems. For example:

at values α=1/540, β=1/1080, we have A-stable scheme with 10-th order of approximating, 

at values α=1/54, β=-1/135, we have L1-stable scheme with 9-th order of approximating, 

L-stability of multi-implicit methods of 8-th order for differential stiff systems by Vasilyev E.I., Vasilyeva T.A., Kiseleva M.N. is licensed under a Creative Commons Attribution 4.0 International License.

at values α=1/54, β=-1/216, we have L2-stable scheme with 8-th order of approximating.
The testing of this difference schemes on linear and non-linear problems with a different stiff power is conducted. The errors of a numerical solution as functions of integration step size are computed in numerical experiments. These results demonstrate high quality of stability and accuracy of the suggested 3ISD-schemes.

Key words: L-stability, А-stability, stiff systems, implicit methods, multiimplicit methods, methods with second derivative.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №1 (18) 2013 pp. 70-83

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