Detail publikace

Modern Taylor series method in numerical integration: PART 2

NEČASOVÁ, G. VEIGEND, P. ŠÁTEK, V.

Originální název

Modern Taylor series method in numerical integration: PART 2

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 with initial condition - initial value problems. Systems of ordinary differential equations are solved using variable order, variable step-size Modern Taylor Series Method. The Modern 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. The paper present the solution of linear and nonlinear problems. As a linear problem, the telegraph equation was chosen. As a nonlinear problem, the behavior of Lorenz system was analyzed. All experiments were performed using MATLAB software, the  newly developed nonlinear solver that uses Modern Taylor Series Method was used. Both linear and nonlinear solvers were compared with state of the art solvers in MATLAB.

Klíčová slova

Taylor series method, ordinary differential equations, technical initial value problems

Autoři

NEČASOVÁ, G.; VEIGEND, P.; ŠÁTEK, V.

Vydáno

22. 1. 2018

Nakladatel

VŠB - Technical University of Ostrava

Místo

Horní Lomná

ISBN

978-80-248-4135-9

Kniha

17th Czech-Polish Conference Modern Mathematical Methods in Engineering (3mi)

Strany od

211

Strany do

220

Strany počet

10

BibTex

@inproceedings{BUT168462,
  author="Gabriela {Nečasová} and Petr {Veigend} and Václav {Šátek}",
  title="Modern Taylor series method in numerical integration: PART 2",
  booktitle="17th Czech-Polish Conference Modern Mathematical Methods in Engineering (3mi)",
  year="2018",
  pages="211--220",
  publisher="VŠB - Technical University of Ostrava",
  address="Horní Lomná",
  isbn="978-80-248-4135-9"
}