Detail publikace

Stability and Convergence of the Modern Taylor Series Method

KUNOVSKÝ, J. SEHNALOVÁ, P. ŠÁTEK, V.

Originální název

Stability and Convergence of the Modern Taylor Series Method

Typ

článek ve sborníku mimo WoS a Scopus

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

KUNOVSKÝ, J.; SEHNALOVÁ, P.; ŠÁTEK, V.

Rok RIV

2010

Vydáno

16. 9. 2010

Nakladatel

Czech Technical University Publishing House

Místo

Praha

ISBN

978-80-01-04589-3

Kniha

Proceedings of the 7th EUROSIM Congress on Modelling and Simulation

Edice

Vol. 2

Strany od

56

Strany do

61

Strany počet

6

BibTex

@inproceedings{BUT34929,
  author="Jiří {Kunovský} and Pavla {Sehnalová} and Václav {Šátek}",
  title="Stability and Convergence of the Modern Taylor Series Method",
  booktitle="Proceedings of the 7th EUROSIM Congress on Modelling and Simulation",
  year="2010",
  series="Vol. 2",
  pages="56--61",
  publisher="Czech Technical University Publishing House",
  address="Praha",
  isbn="978-80-01-04589-3"
}