Project Details

Exploring new Applications for Modern Taylor Series Methods to Solve Stiff and High-Order Systems

Project Period: 1. 7. 2016 – 31. 10. 2017

Project Type: grant

Code: Aktion-76p11

Agency: Ministerstvo školství, mládeže a tělovýchovy ČR

Program: AKTION Česká republika - Rakousko

Czech title
Analýza nových aplikací Moderní metody Taylorovy řady pro řešení tuhých systémů a systémů vysokých řádů
Type
grant
Keywords

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

Abstract

In the two preceding AKTION projects of the partners, the Modern Taylor Series Method (MTSM) could be significantly extended, enriched, validated, and disseminated. These developments provide MTSM-based solvers to produce extremely accurate solutions to stiff systems, discontinuous dynamics, and high-order systems. To further improve MTSM applicability, and to translate its benefits into industrial applications, the project team is expanded to also include the Mechanical Engineering Faculty of TU Brno. Consequently, the international cooperation between TU Wien and TU Brno will be expanded and fostered, new specifically challenging application problems will be studied, and a range of young researchers are given the opportunity to gather international and interdisciplinary experience.

Team members
Kunovský Jiří, doc. Ing., CSc. – research leader
Kocina Filip, Ing., Ph.D.
Nečasová Gabriela, Ing., Ph.D. (DITS)
Rozman Jaroslav, Ing., Ph.D. (DITS)
Šátek Václav, Ing., Ph.D. (DITS)
Veigend Petr, Ing., Ph.D. (DITS)
Zbořil František, doc. Ing., Ph.D. (DITS)
Publications

2018

  • HASLINGER, J.; KUČERA, R.; ŠÁTEK, V.; SASSI, T. Stokes system with solution-dependent threshold slip boundary conditions: Analysis, approximation and implementation. MATHEMATICS AND MECHANICS OF SOLIDS, 2018, vol. 2018, no. 23, p. 294-307. ISSN: 1081-2865. Detail

2017

  • CHALOUPKA, J.; KOCINA, F.; VEIGEND, P.; NEČASOVÁ, G.; ŠÁTEK, V.; KUNOVSKÝ, J. Multiple Integral Computations. In 14th International Conference of Numerical Analysis and Applied Mathematics. AIP conference proceedings. Rhodes: American Institute of Physics, 2017. p. 1-4. ISSN: 0094-243X. Detail
  • CHALOUPKA, J.; NEČASOVÁ, G.; VEIGEND, P.; KUNOVSKÝ, J.; ŠÁTEK, V. Modern Taylor series method in numerical integration: PART 1. 16th Czech-Polish Conference Modern Mathematical Methods in Engineering (3mi). Rybnik: 2017. p. 263-273. ISBN: 978-83-65265-14-2. ISSN: 2391-9361. Detail
  • KOCINA, F.; NEČASOVÁ, G.; VEIGEND, P.; CHALOUPKA, J.; ŠÁTEK, V.; KUNOVSKÝ, J. Modelling VLSI Circuits Using Taylor Series. In 14th International Conference of Numerical Analysis and Applied Mathematics. AIP conference proceedings. Rhodes: American Institute of Physics, 2017. p. 1-4. ISSN: 0094-243X. Detail
  • KUČERA, R.; ŠÁTEK, V.; HASLINGER, J.; POCHYLÝ, F.; KOKO, J.; SASSI, T. Numerical Modelling of the Stokes Flow with Threshold Slip Boundary Conditions. In 14th International Conference of Numerical Analysis and Applied Mathematics. AIP conference proceedings. Rhodes: American Institute of Physics, 2017. p. 1-4. ISSN: 0094-243X. Detail
  • NEČASOVÁ, G.; KOCINA, F.; VEIGEND, P.; CHALOUPKA, J.; ŠÁTEK, V.; KUNOVSKÝ, J. Solving Wave Equation Using Finite Differences and Taylor Series. In 14th International Conference of Numerical Analysis and Applied Mathematics. AIP conference proceedings. Rhodes: American Institute of Physics, 2017. p. 1-4. ISSN: 0094-243X. Detail
  • NEČASOVÁ, G.; KOCINA, F.; VEIGEND, P.; ŠÁTEK, V.; KUNOVSKÝ, J. Model of the Telegraph Line. In Informatics 2017 - 14th International Scientific Conference on Informatics. Poprad: Institute of Electrical and Electronics Engineers, 2017. p. 271-275. ISBN: 978-1-5386-0888-3. Detail
  • VEIGEND, P.; NEČASOVÁ, G.; KOCINA, F.; CHALOUPKA, J.; ŠÁTEK, V.; KUNOVSKÝ, J. Real Time Simulation of Transport Delay. In 14th International Conference of Numerical Analysis and Applied Mathematics. AIP conference proceedings. Rhodes: American Institute of Physics, 2017. p. 1-4. ISSN: 0094-243X. Detail

2016

  • KOCINA, F.; KUNOVSKÝ, J.; NEČASOVÁ, G.; ŠÁTEK, V.; VEIGEND, P. Parallel solution of higher order differential equations. In Proceedings of the 2016 International Conference on High Performance Computing & Simulation (HPCS 2016). Insbruck: Institute of Electrical and Electronics Engineers, 2016. p. 302-309. ISBN: 978-1-5090-2088-1. Detail
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