Conference paperKUNOVSKÝ Jiří, PETŘEK Jiří and ŠÁTEK Václav. Multiple Arithmetic in Dynamic System Simulation. In: Proceedings UKSim 10th International Conference EUROSIM/UKSim2008. Cambridge: IEEE Computer Society, 2008, pp. 597598. ISBN 0769531148.  Publication language:  english 

Original title:  Multiple Arithmetic in Dynamic System Simulation 

Title (cs):  Více slovní aritmetika v simulaci dynamických systémů 

Pages:  597598 

Proceedings:  Proceedings UKSim 10th International Conference EUROSIM/UKSim2008 

Conference:  10th International Conference on Computer Modelling and Simulation 

Place:  Cambridge, GB 

Year:  2008 

ISBN:  0769531148 

Publisher:  IEEE Computer Society 

Keywords 

stiff systems, Modern Taylor series method, differential equations, continuous system modelling, multiple arithmetic

Annotation 

A very interesting and promising numerical method of solving systems of ordinary differential equations based on Taylor series has appeared. The potential of the Taylor series has been exposed by many practical experiments and a way of detection and solution of large systems of ordinary differential equations has been found. Generally speaking, a stiff system contains several components, some of them are heavily suppressed while the rest remain almost unchanged. This feature forces the used method to choose an extremely small integration step and the progress of the computation may become very slow. There are many (implicit) methods for solving stiff systems of ODE's, from the most simple such as implicit Euler method to more sophisticated (implicit RungeKutta methods) and finally the general linear methods. Usually a quite complicated auxiliary system of equations has to be solved in each step. These facts lead to immense amount of work to be done in each step of the computation. These are the reasons why one has to think twice before using the stiff solver and to decide between the stiff and nonstiff solver. 
BibTeX: 

@INPROCEEDINGS{
author = {Ji{\v{r}}{\'{i}} Kunovsk{\'{y}} and Ji{\v{r}}{\'{i}}
Pet{\v{r}}ek and V{\'{a}}clav {\v{S}}{\'{a}}tek},
title = {Multiple Arithmetic in Dynamic System Simulation},
pages = {597598},
booktitle = {Proceedings UKSim 10th International Conference
EUROSIM/UKSim2008},
year = {2008},
location = {Cambridge, GB},
publisher = {IEEE Computer Society},
ISBN = {0769531148},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php.en.iso88592?id=8597}
} 
