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Numerical Integration .NET Graphical Editor
Kučera, Martin ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
This thesis deals with the numerical solution of systems of first-order differential equations with initial conditions, using chosen one-step methods. It describes the design, implementation and testing of the application that is able to use these methods to solve the tasks entered in form of block schemes. The first part is devoted to an introduction of the topic, it provides an example of calculation of several steps using chosen methods and compares the results. A substantial part of the report deals with form and function of each block used in the block schemes editor and the transformation process of input data to data usable for creating simulation. The penultimate chapter demonstrates the accuracy of the final application. It shows solutions of a few simple examples of practical usage. This chapter also includes comparison with other simulation systems.
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Electronic circuits with fractal dynamics
Vojtová, Klára ; Guzan,, Milan (referee) ; Petržela, Jiří (advisor)
In the first section of this work is further analyzed the theories of differential equations and their computation and applications. The second part I addict to more detailed description of the Laplace transform, a sentence that is relevant to this area and also using the Laplace transform to solve electronic circuits. The third part of this project involves the theory of electronic circuits, especially the analysis and synthesis. The final and most important part is attended to circuits with fractal dynamics, design fractal approximation of the dynamics of capacitors in the frequency domain, has finally created its own electronic circuit measurement and evaluation results.
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Parallel/Serial ALU Interconecting System
Sekaninová, Michaela ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This thesis deals with creation of parallel/serial ALU interconecting system. The content of the work is to introduce the issue of interconecting systems and numerical solutions of di fferential equations using Taylor series method. The practical aim of the thesis is to design and implement interconecting system performing calculations of di fferential equations. The system connects integrators automatically by given problem.
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Multiple Integral Effective Computations
Iša, Radek ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
This thesis deals with the design system for multiple integrals for diferential expression with space variables. Today, integration is one of engineering problems. Reader is acquainted with different method of integration, then with numerican integration and Taylor series. The practical aim of this work is to design software and hardware system of numerican integration multiple integrals.
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Numerical methods of solving fractional differential equations
Kyjovský, Adam ; Zatočilová, Jitka (referee) ; Nechvátal, Luděk (advisor)
This bachelor's thesis deals with numerical methods of solving fractional differential equations. Some fundamental notions of fractional calculus and basic results from the theory of fractional differential equations (such as existence and uniqueness of the solution to an initial value problem with the Caputo derivative) are presented. Further, a summary of selected numerical methods for solving such initial value problems is presented. These methods are tested and compared on a model problem.
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Adjoint Differential Equations
Kmenta, Karel ; Pindryč, Milan (referee) ; Kunovský, Jiří (advisor)
This project deals with solving differential equations. The aim is find the correct algorithm transforming differential equations of higher order with time variable coefficients to equivalent systems of differential equations of first order. Subsequently verify its functionality for equations containing the involutioin goniometrical functions and finally implement this algorithm. The reason for this transformation is requirement to solve these differential equations by programme TKSL (Taylor Kunovský simulation language).
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Electronic Circuits Simulations and Parasitic Inductances
Ševčík, Roman ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work deals with the solution of differential equations and systems of differential equations through the use of parasitic inductances. Thus obtained equations serve as input data for the simulation tool TKSL, which allows their solutions using the Taylor series. Furthermore, according to the proposal in C# is implemented a system for graphic display output data from TKSL. The system makes it possible to view trending as a continuous two-dimensional graphs.
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Implementation of a Language Interpreter for Mathematical Calculations
Kobelka, Martin ; Šátek, Václav (referee) ; Veigend, Petr (advisor)
The main goal of this bachelor thesis is to design and implement the new programing language, which can be used for mathematical computations, implement the demonstration interpret of this language and design a graphical user interface for it. The user interface makes it easy to write the calculation, enables effective and clear visualization of calculation results and basic debugging of calculation. The properties of the resulting language are described in the thesis with the several experiments with the interpret, which implements a~subset of the language. Differences between designed solution and other platforms are also described in the thesis.
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Estimation of Solutions of Differential Systems with Delayed Argument of Neutral Type
Baštincová, Alena ; Růžičková, Miroslava (referee) ; Dzhalladova,, Irada (referee) ; Diblík, Josef (advisor)
Tato disertační práce pojednává o řešení diferenciálních rovnic a systémů diferenciálních rovnic. Hlavní pozornost je věnována asymptotickým vlastnostem rovnic se zpožděním a systémů rovnic se zpožděním. V první kapitole jsou uvedeny fyzikální a technické příklady popsané pomocí diferenciálních rovnic se zpožděním a jejich systémů. Je uvedena klasifikace rovnic se zpožděním a jsou zformulovány základní pojmy stability s důrazem na druhou metodu Ljapunova. Ve druhé kapitole jsou studovány odhady řešení rovnic neutrálního typu. Třetí kapitola se zabývá systémy diferenciálních rovnic neutrálního typu. Jsou odvozeny asymptotické odhady pro řešení i pro derivace řešení. V závěru kapitoly jsou uvedeny příklady a srovnání výsledků s pracemi jiných autorů. Výpočty byly prováděny pomocí programu MATLAB. Poslední, čtvrtá kapitola, se zabývá asymptotickými vlastnostmi systémů se speciálním typem nelinearity, tzv. sektorové nelinearity. Jsou odvozeny vlastnosti řešení a derivace řešení. Základní metodou pro důkazy je v celé práci druhá Ljapunovova metoda a použití funkcionálů Ljapunova-Krasovského.
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Multiple Operation Simulation
Závada, Vladislav ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work deals with the numeric integration. The reader is acquainted with the numerical solution of differential equations using Taylor series method. Then describes the different variants integrators. The practical part describes the design double-input integrator with multiplication and its implementation in an FPGA. For this integrator is also provided a simulator demonstrate its function.
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