Ing. Gabriela Nečasová
CHALOUPKA Jan, NEČASOVÁ Gabriela, VEIGEND Petr, KUNOVSKÝ Jiří and ŠÁTEK Václav. Modern Taylor series method in numerical integration: PART 1. In: 16th CzechPolish Conference Modern Mathematical Methods in Engineering (3mi). Rybnik, 2017, pp. 263273. ISBN 9788365265142. ISSN 23919361.  Publication language:  english 

Original title:  Modern Taylor series method in numerical integration: PART 1 

Pages:  263273 

Proceedings:  16th CzechPolish Conference Modern Mathematical Methods in Engineering (3mi) 

Conference:  Modern Mathematical Methods in Engineeering 

Place:  Rybnik, PL 

Year:  2017 

ISBN:  9788365265142 

Journal:  Systemy Wspomagania w Inżynierii Produkcji, Vol. 6, No. 4, Gliwice, PL 

ISSN:  23919361 

Keywords 

Taylor series method; ordinary differential equations; technical initial value problems 
Annotation 

The paper deals with extremely exact, stable and fast numerical solutions of systems of differential equations. It also involves solutions of problems that can be reduced to solving a system of differential equations. The approach is based on an original mathematical method, which uses the Taylor series method for solving differential equations in a nontraditional way. Even though this method is not much preferred in the literature, experimental calculations have verified that the accuracy and stability of the Taylor series method exceed the currently used algorithms for numerically solving differential equations. The Modern Taylor Series Method (MTSM) is based on a recurrent calculation of the Taylor series terms for each time interval. Thus, the complicated calculation of higher order derivatives (much criticised in the literature) need not be performed but rather the value of each Taylor series term is numerically calculated. An important part of the method is an automatic integration order setting, i.e. using as many Taylor series terms as the defined accuracy requires.
The aim of our research is to propose the extremely exact, stable and fast numerical solver for modelling of technical initial value problems that offers wide applications in many engineering areas including modelling of electrical circuits, mechanics of rigid bodies, control loop feedback (controllers), etc. 
BibTeX: 

@INPROCEEDINGS{
author = {Jan Chaloupka and Gabriela Ne{\v{c}}asov{\'{a}}
and Petr Veigend and Ji{\v{r}}{\'{i}}
Kunovsk{\'{y}} and V{\'{a}}clav {\v{S}}{\'{a}}tek},
title = {Modern Taylor series method in numerical
integration: PART 1},
pages = {263273},
booktitle = {16th CzechPolish Conference Modern Mathematical Methods in
Engineering (3mi)},
journal = {Systemy Wspomagania w In{\'{z}}ynierii Produkcji},
volume = 6,
number = 4,
year = 2017,
location = {Rybnik, PL},
ISBN = {9788365265142},
ISSN = {23919361},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php?id=11354}
} 
