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Numerical Integrators Development Environment
Vopěnka, Václav ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This term project describes transformation of system of diferential equations into polynomial form. Such transformed systems of diferential equations can be subsequently solved using Taylor series. This method enables computing of initial problem's numeric solution using dynamical order selection in order to achieve required accuracy. The work mathematically proves, that transformed systems of diferential equations have the same solution as the original systems. This transformation can be used for all mathematic functions commonly used in technical applications. The work also focuses on optimization of given problem and implements it in programme taylor. This progamme enables user to solve given diferential equations with chosen parameters.
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Numerical Integrators Development Environment
Vopěnka, Václav ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This term project describes transformation of system of diferential equations into polynomial form. Such transformed systems of diferential equations can be subsequently solved using Taylor series. This method enables computing of initial problem's numeric solution using dynamical order selection in order to achieve required accuracy. The work mathematically proves, that transformed systems of diferential equations have the same solution as the original systems. This transformation can be used for all mathematic functions commonly used in technical applications. The work also focuses on optimization of given problem and implements it in programme taylor. This progamme enables user to solve given diferential equations with chosen parameters.
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