Detail publikace

Initial Problems with Polynomials on Right-hand Sides

KALUŽA, V. KRAUS, M. KUNOVSKÝ, J. ŠÁTEK, V.

Originální název

Initial Problems with Polynomials on Right-hand Sides

Anglický název

Initial Problems with Polynomials on Right-hand Sides

Jazyk

en

Originální abstrakt

As long as 250 years ago the method of Taylor series was already well developed. Since then the application of Taylor series has become a standard concept in numerical analysis. Their ability of approximating functions arbitrarily close under certain conditions makes them, at least theoretically, an ideal tool for the integration of differential equations. Before the appearance of digital computers the analytical determination of Taylor series coefficients, i.e. the calculation of higher derivatives, was regarded as too complicated in most cases. In many modern text books [3], [4] on numerical or applied mathematics has even been stated that Taylor series, although theoretically and conceptually very interesting, can only be applied as implementation in very special cases, since a general purpose integration algorithm is too complicated or even impossible. In this paper an outline is presented of establishing Taylor series coefficients of initial problems with polynomials on right-hand sides. The application of recurrent Taylor series to the integration of systems of ordinary differential equations is discused. The software TKSL for the solution of initial value problems by means of recurrent Taylor series has been developed and many positive results have been obtained [5]. TKSL is available for those interested.

Anglický abstrakt

As long as 250 years ago the method of Taylor series was already well developed. Since then the application of Taylor series has become a standard concept in numerical analysis. Their ability of approximating functions arbitrarily close under certain conditions makes them, at least theoretically, an ideal tool for the integration of differential equations. Before the appearance of digital computers the analytical determination of Taylor series coefficients, i.e. the calculation of higher derivatives, was regarded as too complicated in most cases. In many modern text books [3], [4] on numerical or applied mathematics has even been stated that Taylor series, although theoretically and conceptually very interesting, can only be applied as implementation in very special cases, since a general purpose integration algorithm is too complicated or even impossible. In this paper an outline is presented of establishing Taylor series coefficients of initial problems with polynomials on right-hand sides. The application of recurrent Taylor series to the integration of systems of ordinary differential equations is discused. The software TKSL for the solution of initial value problems by means of recurrent Taylor series has been developed and many positive results have been obtained [5]. TKSL is available for those interested.

Dokumenty

BibTex

``````
@inproceedings{BUT33784,
author="Vlastimil {Kaluža} and Michal {Kraus} and Jiří {Kunovský} and Václav {Šátek}",
title="Initial Problems with Polynomials on Right-hand Sides",
annote="As long as 250 years ago the method of Taylor series was already well developed.
Since then the application of Taylor series has become a standard concept in
numerical analysis. Their ability of approximating functions arbitrarily close
under certain conditions makes them, at least theoretically, an ideal tool for
the integration of differential equations.
Before the appearance of digital computers the analytical determination of Taylor
series coefficients, i.e. the calculation of higher derivatives, was regarded as
too complicated in most cases. In many modern text books [3], [4] on numerical or
applied mathematics has even been stated that Taylor series, although
theoretically and conceptually very interesting, can only be applied as
implementation in very special cases, since a general purpose integration
algorithm is too complicated or even impossible.
In this paper an outline is presented of establishing Taylor series coefficients
of initial problems with polynomials on right-hand sides. The application of
recurrent Taylor series to the integration of systems of ordinary differential
equations is discused. The software TKSL for the solution of initial value
problems by means of recurrent Taylor series has been developed and many positive
results have been obtained [5]. TKSL is available for those interested.",