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CHALOUPKA, J. NEČASOVÁ, G. VEIGEND, P. KUNOVSKÝ, J. ŠÁTEK, V.
Original Title
Modern Taylor series method in numerical integration: PART 1
Type
article in a collection out of WoS and Scopus
Language
English
Original Abstract
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.
Keywords
Taylor series method; ordinary differential equations; technical initial value problems
Authors
CHALOUPKA, J.; NEČASOVÁ, G.; VEIGEND, P.; KUNOVSKÝ, J.; ŠÁTEK, V.
Released
7. 6. 2017
Location
Rybnik
ISBN
978-83-65265-14-2
Book
16th Czech-Polish Conference Modern Mathematical Methods in Engineering (3mi)
2391-9361
Year of study
6
Number
4
Pages from
263
Pages to
273
Pages count
11
BibTex
@inproceedings{BUT168452, author="Jan {Chaloupka} and Gabriela {Nečasová} and Petr {Veigend} and Jiří {Kunovský} and Václav {Šátek}", title="Modern Taylor series method in numerical integration: PART 1", booktitle="16th Czech-Polish Conference Modern Mathematical Methods in Engineering (3mi)", year="2017", volume="6", number="4", pages="263--273", address="Rybnik", isbn="978-83-65265-14-2", issn="2391-9361" }