Vasilev E.I., Vasilyeva T.A., Kiseleva M.N. Multi-implicit SD-methods for stiff systems of differential equations

 

Vasilev Evgeniy Ivanovich
 
Doctor of Physics and Mathematics, Professor, Chair of Fundamental Information Science and Optimal Control, Volgograd State University
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Prospect Universitetsky, 100, 400062 Volgograd, Russian Federation
 
Vasilyeva Tatiana Anatolievna
 
Candidate of Physics and Mathematics, Associate Professor, Chair of Fundamental Information Science and Optimal Control, Volgograd State University
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Prospect Universitetsky, 100, 400062 Volgograd, Russian Federation
 
Kiseleva Maria Nikolaevna
 
Master Student in “Applied Mathematics and Informatics”, V olgograd State University
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Prospect Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. The new set of absolutely stable difference schemes for a numerical solution of ODEs stiff systems is submitted. The main feature of the set is the multi-implicit finite differences with the second derivatives of the desired solution. The schemes with 4, 6 and 8 orders of accuracy in detail are considered. The testing results of difference schemes on the Hill’s problem and the Kreiss stiff system are shown. The procedure of automatic selection of an integration step with the control of accuracy is submitted. The considerable advantage in efficiency of the high order schemes with the automatic step selection is shown.

Key words: finite difference schemes, stiff systems, implicit methods, multi-implicit methods, methods with second derivative, accuracy control, step selection.

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Multi-implicit SD-methods for stiff systems of differential equations by Vasilev E.I., Vasilyeva T.A., Kiseleva M.N. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №2 (17) 2012 pp. 68-77

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