"Numerick\u00E9 \u0159e\u0161en\u00ED soustav oby\u010Dejn\u00FDch diferenci\u00E1ln\u00EDch rovnic v modelov\u00E1n\u00ED a simulaci"@cs . "Numerical solution of systems of ordinary differential equations in modeling and simulation"@en . . "RIV/70883521:28140/14:43871274" . "Vogeltanz, Tom\u00E1\u0161" . . . . . . . "Numerick\u00E9 \u0159e\u0161en\u00ED soustav oby\u010Dejn\u00FDch diferenci\u00E1ln\u00EDch rovnic v modelov\u00E1n\u00ED a simulaci" . "CZ - \u010Cesk\u00E1 republika" . "S" . "Trilobit" . . "Tato pr\u00E1ce pojedn\u00E1v\u00E1 o nej\u010Dast\u011Bji vyu\u017E\u00EDvan\u00FDch numerick\u00FDch metod\u00E1ch p\u0159i \u0159e\u0161en\u00ED soustav oby\u010Dejn\u00FDch diferenci\u00E1ln\u00EDch rovnic v modelov\u00E1n\u00ED a simulaci syst\u00E9m\u016F. Cel\u00E1 \u0159ada \u00FAloh, kter\u00E9 se vyskytuj\u00ED v modelov\u00E1n\u00ED a simulac\u00ED syst\u00E9m\u016F, nen\u00ED analyticky \u0159e\u0161iteln\u00E1 nebo je nalezen\u00ED p\u0159esn\u00E9ho \u0159e\u0161en\u00ED p\u0159\u00EDli\u0161 obt\u00ED\u017En\u00E9. Numerick\u00E1 matematika se v t\u011Bchto p\u0159\u00EDpadech sna\u017E\u00ED nal\u00E9zt alespo\u0148 \u0159e\u0161en\u00ED p\u0159ibli\u017En\u00E9. Na za\u010D\u00E1tku t\u00E9to pr\u00E1ce je uveden popis soustav oby\u010Dejn\u00FDch diferenci\u00E1ln\u00EDch rovnic a jejich numerick\u00E9ho \u0159e\u0161en\u00ED. Hlavn\u00ED \u010D\u00E1st popisuje Eulerovy a Runge-Kuttovy numerick\u00E9 metody, kter\u00E9 se nej\u010Dast\u011Bji vyu\u017E\u00EDvaj\u00ED pro \u0159e\u0161en\u00ED oby\u010Dejn\u00FDch diferenci\u00E1ln\u00EDch rovnic, a to v\u010Detn\u011B uveden\u00ED odhadu chyb a stability t\u011Bchto metod." . "http://trilobit.fai.utb.cz/numericke-reseni-soustav-obycejnych-diferencialnich-rovnic-v-modelovani-a-simulaci_36b32c3c-65a8-478d-9f4f-f01880a99a61" . "33402" . . . "Numerick\u00E9 \u0159e\u0161en\u00ED soustav oby\u010Dejn\u00FDch diferenci\u00E1ln\u00EDch rovnic v modelov\u00E1n\u00ED a simulaci"@cs . . . . "9"^^ . . . "28140" . "2"^^ . . "2"^^ . . "Tato pr\u00E1ce pojedn\u00E1v\u00E1 o nej\u010Dast\u011Bji vyu\u017E\u00EDvan\u00FDch numerick\u00FDch metod\u00E1ch p\u0159i \u0159e\u0161en\u00ED soustav oby\u010Dejn\u00FDch diferenci\u00E1ln\u00EDch rovnic v modelov\u00E1n\u00ED a simulaci syst\u00E9m\u016F. Cel\u00E1 \u0159ada \u00FAloh, kter\u00E9 se vyskytuj\u00ED v modelov\u00E1n\u00ED a simulac\u00ED syst\u00E9m\u016F, nen\u00ED analyticky \u0159e\u0161iteln\u00E1 nebo je nalezen\u00ED p\u0159esn\u00E9ho \u0159e\u0161en\u00ED p\u0159\u00EDli\u0161 obt\u00ED\u017En\u00E9. Numerick\u00E1 matematika se v t\u011Bchto p\u0159\u00EDpadech sna\u017E\u00ED nal\u00E9zt alespo\u0148 \u0159e\u0161en\u00ED p\u0159ibli\u017En\u00E9. Na za\u010D\u00E1tku t\u00E9to pr\u00E1ce je uveden popis soustav oby\u010Dejn\u00FDch diferenci\u00E1ln\u00EDch rovnic a jejich numerick\u00E9ho \u0159e\u0161en\u00ED. Hlavn\u00ED \u010D\u00E1st popisuje Eulerovy a Runge-Kuttovy numerick\u00E9 metody, kter\u00E9 se nej\u010Dast\u011Bji vyu\u017E\u00EDvaj\u00ED pro \u0159e\u0161en\u00ED oby\u010Dejn\u00FDch diferenci\u00E1ln\u00EDch rovnic, a to v\u010Detn\u011B uveden\u00ED odhadu chyb a stability t\u011Bchto metod."@cs . "[46970430AFB7]" . "Ja\u0161ek, Roman" . "This paper discusses the most common numerical methods used to solve systems of ordinary differential equations in modeling and simulation. A number of tasks which occur in modeling and simulation cannot be solved analytically or it is too difficult to find their exact solution. In these cases, numerical mathematics tries to find at least approximate solution. At the beginning of this paper the description of systems of ordinary differential equations and their numerical solution are shown. In the main section, the Euler and Runge-Kutta methods, which are the most commonly used numerical methods for finding the solution of ordinary differential equations, are described, including the error estimates and stability."@en . . "Numerick\u00E9 \u0159e\u0161en\u00ED soustav oby\u010Dejn\u00FDch diferenci\u00E1ln\u00EDch rovnic v modelov\u00E1n\u00ED a simulaci" . "RIV/70883521:28140/14:43871274!RIV15-MSM-28140___" . "Numerical solution of systems of ordinary differential equations in modeling and simulation"@en . "1804-1795" . "2014" . "1" . "Numerical Methods, Ordinary Differential Equations, Euler Method, Runge-Kutta Methods, Modeling, Simulation"@en .