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

Czech title:Analýza nových aplikací Moderní metody Taylorovy řady pro řešení tuhých systémů a systémů vysokých řádů
Reseach leader:Kunovský Jiří
Team members:Kocina Filip, Nečasová Gabriela, Rozman Jaroslav, Šátek Václav, Veigend Petr, Zbořil František
Agency:Ministry of Education, Youth and Sports Czech Republic
Code:Aktion-76p11
Start:2016-07-01
End:2017-10-31
Keywords:numerical integration methods, parallel computations, differential equations, large systems of algebraic equations, Taylor series
Annotation:
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.

Publications

2017CHALOUPKA Jan, KOCINA Filip, VEIGEND Petr, NEČASOVÁ Gabriela, ŠÁTEK Václav and KUNOVSKÝ Jiří. Multiple Integral Computations. In: 14th International Conference of Numerical Analysis and Applied Mathematics. Rhodes: American Institute of Physics, 2017, pp. 1-4. ISSN 0094-243X.
 CHALOUPKA Jan, NEČASOVÁ Gabriela, VEIGEND Petr, KUNOVSKÝ Jiří and ŠÁTEK Václav. Modern Taylor series method in numerical integration: PART 1. In: 16th Czech-Polish Conference Modern Mathematical Methods in Engineering (3mi). Rybnik, 2017, pp. 263-273. ISBN 978-83-65265-14-2. ISSN 2391-9361.
 KOCINA Filip, NEČASOVÁ Gabriela, VEIGEND Petr, CHALOUPKA Jan, ŠÁTEK Václav and KUNOVSKÝ Jiří. Modelling VLSI Circuits Using Taylor Series. In: 14th International Conference of Numerical Analysis and Applied Mathematics. Rhodes: American Institute of Physics, 2017, pp. 1-4. ISSN 0094-243X.
 KUČERA Radek, ŠÁTEK Václav, HASLINGER Jaroslav, POCHYLÝ František, KOKO Jonas and SASSI Taoufik. Numerical Modelling of the Stokes Flow with Threshold Slip Boundary Conditions. In: 14th International Conference of Numerical Analysis and Applied Mathematics. Rhodes: American Institute of Physics, 2017, pp. 1-4. ISSN 0094-243X.
 NEČASOVÁ Gabriela, KOCINA Filip, VEIGEND Petr, CHALOUPKA Jan, ŠÁTEK Václav and KUNOVSKÝ Jiří. Solving Wave Equation Using Finite Differences and Taylor Series. In: 14th International Conference of Numerical Analysis and Applied Mathematics. Rhodes: American Institute of Physics, 2017, pp. 1-4. ISSN 0094-243X.
 VEIGEND Petr, NEČASOVÁ Gabriela, KOCINA Filip, CHALOUPKA Jan, ŠÁTEK Václav and KUNOVSKÝ Jiří. Real Time Simulation of Transport Delay. In: 14th International Conference of Numerical Analysis and Applied Mathematics. Rhodes: American Institute of Physics, 2017, pp. 1-4. ISSN 0094-243X.
2016KOCINA Filip, KUNOVSKÝ Jiří, NEČASOVÁ Gabriela, ŠÁTEK Václav and VEIGEND Petr. 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, pp. 302-309. ISBN 978-1-5090-2088-1.

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