Conference paperKUNOVSKÝ Jiří, SEHNALOVÁ Pavla and ŠÁTEK Václav. Stability and Convergence of the Modern Taylor Series Method. In: Proceedings of the 7th EUROSIM Congress on Modelling and Simulation. Praha: Czech Technical University Publishing House, 2010, p. 6. ISBN 9788001045893.  Publication language:  english 

Original title:  Stability and Convergence of the Modern Taylor Series Method 

Title (cs):  Stabilita a Konvergence Metody Moderní Taylorovy Řady 

Pages:  6 

Proceedings:  Proceedings of the 7th EUROSIM Congress on Modelling and Simulation 

Conference:  7th EUROSIM Congress on Modelling and Simulation (2010) 

Series:  Vol. 2 

Place:  Praha, CZ 

Year:  2010 

ISBN:  9788001045893 

Publisher:  Czech Technical University Publishing House 

Keywords 

Stability, Convergence, Modern Taylor Series Method, Differential equations, Continuous system modelling 
Annotation 

The paper deals with extremely exact, stable and fast numerical
solutions of systems of differential equations. In a natural way, it
also involves solutions of problems that can be transformed to solving a
system of differential equations. The project is based on an
original mathematical method which uses the Taylor series method for
solving differential equations. The Taylor Series Method is based on a
recurrent calculation of the Taylor series terms for each time
interval. Thus the complicated calculation of higher order derivatives
(much criticized in the literature) need not be performed but rather the
value of each Taylor series term is numerically calculated. Another
typical algorithm is the convolution operation. Stability and
convergence of the numerical integration methods when the Dahlquist
problem is solved, Taylorian initial problems with automatic
transformation, stability and convergence of a system of linear
algebraic equations and stability and convergence when algebraic and
transcendental equations are solved is discussed in this paper. 
BibTeX: 

@INPROCEEDINGS{
author = {Ji{\v{r}}{\'{i}} Kunovsk{\'{y}} and Pavla Sehnalov{\'{a}}
and V{\'{a}}clav {\v{S}}{\'{a}}tek},
title = {Stability and Convergence of the Modern Taylor Series Method},
pages = {6},
booktitle = {Proceedings of the 7th EUROSIM Congress on Modelling and
Simulation},
series = {Vol. 2},
year = {2010},
location = {Praha, CZ},
publisher = {Czech Technical University Publishing House},
ISBN = {9788001045893},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php?id=9328}
} 
