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Runge-Kutta methods Kroulíková, Tereza ; Nechvátal, Luděk (referee) ; Zatočilová, Jitka (advisor) Tato práce se zabývá Runge--Kuttovými metodami pro počáteční problém. Práce začíná analýzou Eulerovy metody a odvozením podmínek řádu. Jsou představeny modifikované metody. Pro dvě z nich je určen jejich řád teoreticky a pro všechny je provedeno numerické testování řádu. Jsou představeny a numericky testovány dva typy metod s odhadem chyby, "embedded" metody a metody založené na modifikovaných metodách. V druhé části jsou odvozeny implicitní metody. Jsou představeny dva způsoby konstrukce implicitních "embedded" metod. Jsou zmíněny také diagonální implicitní metody. Na závěr jsou probrány dva druhy stability u metod prezentovaných v práci. Detailed record

Runge-Kutta methods Kroulíková, Tereza ; Nechvátal, Luděk (referee) ; Zatočilová, Jitka (advisor) Tato práce se zabývá Runge--Kuttovými metodami pro počáteční problém. Práce začíná analýzou Eulerovy metody a odvozením podmínek řádu. Jsou představeny modifikované metody. Pro dvě z nich je určen jejich řád teoreticky a pro všechny je provedeno numerické testování řádu. Jsou představeny a numericky testovány dva typy metod s odhadem chyby, "embedded" metody a metody založené na modifikovaných metodách. V druhé části jsou odvozeny implicitní metody. Jsou představeny dva způsoby konstrukce implicitních "embedded" metod. Jsou zmíněny také diagonální implicitní metody. Na závěr jsou probrány dva druhy stability u metod prezentovaných v práci. Detailed record

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