Faculty of Information Technology, BUT

Publication Details

Stiff Systems Analysis

ŠÁTEK Václav. Stiff Systems Analysis. Information Sciences and Technologies Bulletin of the ACM Slovakia, vol. 4, no. 3, pp. 1-11. ISSN 1338-1237. Available from: http://acmbulletin.fiit.stuba.sk/vol4num3/vol4num3.pdf
Czech title
Analýza Stiff soustav diferenciálních rovnic
Type
journal article
Language
english
Authors
URL
Keywords
Stiff Systems of Differential Equations, Taylor Series Method, Ordinary Differential Equations, Initial Value Problems, Numerical Solutions of Differential Equations, TKSL software
Abstract
The paper deals with stiff systems of differential equations. To solve this sort of system numerically is a diffult task. In spite of the fact that we come across stiff systems quite often in the common practice, a very interesting and promissing numerical method of solving systems of ordinary differential equations (ODE) based on Taylor series has appeared. The question was how to harness the said "Modern Taylor Series Method" (MTSM) for solving of stiff systems.

The potential of the Taylor series has been exposed by many practical experiments and a way of detection and explicit solution of large systems of ODE has been found. Detailed analysis of stability and convergence of explicit and implicit Taylor series is presented and a new algorithm using implicit Taylor series based on recurrent calculation of Taylor series terms and Newton iteration method (ITMRN) is described. The new method reducing stiffness in system based on finding new equivalent system of ODE "without stiffness" is introduced.

Published
2012
Pages
1-11
Journal
Information Sciences and Technologies Bulletin of the ACM Slovakia, vol. 4, no. 3, ISSN 1338-1237
Book
Information Sciences and Technologies Bulletin of the ACM Slovakia
Publisher
Vydavateľstvo STU
Place
Bratislava, SK
BibTeX
@ARTICLE{FITPUB10164,
   author = "V\'{a}clav \v{S}\'{a}tek",
   title = "Stiff Systems Analysis",
   pages = "1--11",
   booktitle = "Information Sciences and Technologies Bulletin of the ACM Slovakia",
   journal = "Information Sciences and Technologies Bulletin of the ACM Slovakia",
   volume = 4,
   number = 3,
   year = 2012,
   location = "Bratislava, SK",
   ISSN = "1338-1237",
   language = "english",
   url = "https://www.fit.vut.cz/research/publication/10164"
}
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