Publication detail

Stability and Convergence of the Modern Taylor Series Method

KUNOVSKÝ, J. SEHNALOVÁ, P. ŠÁTEK, V.

Original Title

Stability and Convergence of the Modern Taylor Series Method

English Title

Stability and Convergence of the Modern Taylor Series Method

Type

conference paper

Language

en

Original Abstract

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.

English abstract

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.

Keywords

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

RIV year

2010

Released

16.09.2010

Publisher

Czech Technical University Publishing House

Location

Praha

ISBN

978-80-01-04589-3

Book

Proceedings of the 7th EUROSIM Congress on Modelling and Simulation

Edition

Vol. 2

Edition number

NEUVEDEN

Pages from

56

Pages to

61

Pages count

6

Documents

BibTex


@inproceedings{BUT34929,
  author="Jiří {Kunovský} and Pavla {Sehnalová} and Václav {Šátek}",
  title="Stability and Convergence of the Modern Taylor Series Method",
  annote="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.",
  address="Czech Technical University Publishing House",
  booktitle="Proceedings of the 7th EUROSIM Congress on Modelling and Simulation",
  chapter="34929",
  edition="Vol. 2",
  howpublished="print",
  institution="Czech Technical University Publishing House",
  year="2010",
  month="september",
  pages="56--61",
  publisher="Czech Technical University Publishing House",
  type="conference paper"
}