Conference paperKALUŽA Vlastimil, KRAUS Michal, KUNOVSKÝ Jiří and ŠÁTEK Václav. Initial Problems with Polynomials on Righthand Sides. In: Proceedings of Third Asia International Conference on Modelling and Simulation. Bandung/Bali: IEEE Computer Society, 2009, pp. 182187. ISBN 9780769536484.  Publication language:  english 

Original title:  Initial Problems with Polynomials on Righthand Sides 

Title (cs):  Počáteční problémy s polynomy 

Pages:  182187 

Proceedings:  Proceedings of Third Asia International Conference on Modelling and Simulation 

Conference:  Third Asia International Conference on Modelling & Simulation 

Place:  Bandung/Bali, ID 

Year:  2009 

ISBN:  9780769536484 

Publisher:  IEEE Computer Society 

Keywords 

ordinary differential equations, TKSL, Taylor series method

Annotation 

As long as 250 years ago the method of Taylor series was already well developed. Since then the application of Taylor series has become a standard concept in numerical analysis. Their ability of approximating functions arbitrarily close under certain conditions makes them, at least theoretically, an ideal tool for the integration of differential equations. Before the appearance of digital computers the analytical determination of Taylor series coefficients, i.e. the calculation of higher derivatives, was regarded as too complicated in most cases. In many modern text books [3], [4] on numerical or applied mathematics has even been stated that Taylor series, although theoretically and conceptually very interesting, can only be applied as implementation in very special cases, since a general purpose integration algorithm is too complicated or even impossible. In this paper an outline is presented of establishing Taylor series coefficients of initial problems with polynomials on righthand sides. The application of recurrent Taylor series to the integration of systems of ordinary differential equations is discused. The software TKSL for the solution of initial value problems by means of recurrent Taylor series has been developed and many positive results have been obtained [5]. TKSL is available for those interested. 
BibTeX: 

@INPROCEEDINGS{
author = {Vlastimil Kalu{\v{z}}a and Michal Kraus and Ji{\v{r}}{\'{i}}
Kunovsk{\'{y}} and V{\'{a}}clav {\v{S}}{\'{a}}tek},
title = {Initial Problems with Polynomials on Righthand Sides},
pages = {182187},
booktitle = {Proceedings of Third Asia International Conference on
Modelling and Simulation},
year = {2009},
location = {Bandung/Bali, ID},
publisher = {IEEE Computer Society},
ISBN = {9780769536484},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php?id=8958}
} 
