Project Details

Modern Taylor Series Method and Parallel Implementation of Numerical Methods for Large Systems

Project Period: 10. 2. 2014 – 30. 4. 2015

Project Type: grant

Code: Aktion

Agency: Ministerstvo školství, mládeže a tělovýchovy ČR

Program: AKTION Česká republika - Rakousko

Czech title
Moderní metoda Taylorovy řady a paralelní implementace numerických metod pro rozsáhlé soustavy
Type
grant
Keywords

numerical integration methods, parallel computations, differential equations, large systems of algebraic equations, Taylor series

Abstract

The project will extend the results of the preceding Aktion-64p13 project. New efficient algorithms will be devised and implemented of sophisticated simulation problems focusing on methods of parallel computation. The extreme precision will be verified of the Modern Taylor series Method (MTSM) applied to mathematical problems (large systems of ordinary differential equations, repeated integrals, partial differential equations) solving tasks of the theory of control and the theory of flows (large systems of algebraic equations). The results of the proposed project will enable both research groups to build up advanced knowledge on solving demanding simulation problems and to establish suitable solver tools for typical research problems.

Team members
Kunovský Jiří, doc. Ing., CSc. – research leader
Chaloupka Jan, Ing.
Kocina Filip, Ing., Ph.D.
Šátek Václav, Ing., Ph.D. (DITS)
Publications

2015

  • KOCINA, F.; ŠÁTEK, V.; VEIGEND, P.; NEČASOVÁ, G.; VALENTA, V.; KUNOVSKÝ, J. New Trends in Taylor Series Based Applications. In 13rd International Conference of Numerical Analysis and Applied Mathematics. AIP conference proceedings. Rhodes: American Institute of Physics, 2015. p. 1-4. ISBN: 978-0-7354-1287-3. ISSN: 0094-243X. Detail
  • NEČASOVÁ, G.; KUNOVSKÝ, J.; ŠÁTEK, V.; CHALOUPKA, J.; VEIGEND, P. Taylor Series Based Differential Formulas. In MATHMOD VIENNA 2015 - 8th Vienna Conference on Mathematical Modelling. ARGESIM REPORT No. 44. Vienna: ARGE Simulation News, 2015. p. 705-706. ISBN: 978-3-901608-46-9. Detail
  • ŠÁTEK, V.; KOCINA, F.; KUNOVSKÝ, J.; SCHIRRER, A. Taylor Series Based Solution of Linear ODE Systems and MATLAB Solvers Comparison. In MATHMOD VIENNA 2015 - 8th Vienna Conference on Mathematical Modelling. ARGESIM REPORT No. 44. Vienna: ARGE Simulation News, 2015. p. 693-694. ISBN: 978-3-901608-46-9. Detail
  • VEIGEND, P.; KUNOVSKÝ, J.; KOCINA, F.; NEČASOVÁ, G.; ŠÁTEK, V.; VALENTA, V. Electronic Representation of Wave Equation. In 13rd International Conference of Numerical Analysis and Applied Mathematics. AIP conference proceedings. Rhodes: American Institute of Physics, 2015. p. 1-4. ISBN: 978-0-7354-1392-4. ISSN: 0094-243X. Detail
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