Conference paper

CHALOUPKA Jan, NEČASOVÁ Gabriela, VEIGEND Petr, KUNOVSKÝ Jiří and ŠÁTEK Václav. Modern Taylor series method in numerical integration: PART 1. In: 16th Czech-Polish Conference Modern Mathematical Methods in Engineering (3mi). Rybnik, 2017, pp. 263-273. ISBN 978-83-65265-14-2. ISSN 2391-9361.
Publication language:english
Original title:Modern Taylor series method in numerical integration: PART 1
Pages:263-273
Proceedings:16th Czech-Polish Conference Modern Mathematical Methods in Engineering (3mi)
Conference:Modern Mathematical Methods in Engineeering
Place:Rybnik, PL
Year:2017
ISBN:978-83-65265-14-2
Journal:Systemy Wspomagania w Inżynierii Produkcji, Vol. 6, No. 4, Gliwice, PL
ISSN:2391-9361
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 non-traditional 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 = {263--273},
   booktitle = {16th Czech-Polish 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 = {978-83-65265-14-2},
   ISSN = {2391-9361},
   language = {english},
   url = {http://www.fit.vutbr.cz/research/view_pub.php?id=11354}
}

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