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Electric Circuits Simulations in a Specialized Parallel System
Janko, Roman ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work provides an overview of methods for the numerical solution of differential equations. Options of their parallelization, a division of computational operations on multiple microprocessors, are provided with emphasis placed on the Taylor series. The next part of the work is devoted to the description of a specialized parallel system, which was design to fast solving of these equations. Differential equations are appropriate to describe electrical circuits. An important characteristic of each circuit is its behavior in the frequency domain. The aim of this thesis was to design and implement a program which investigate frequency characteristics of AC circuits. A method for analyzing a circuit and automatically assembling corresponding equations is presented. These differential equations are then solved in TKSL. At the end of this work a time consumption is evaluated and compared with Matlab.
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Semi-Analytical Computations
Herzallah, Ahmad Sudqi Hussein ; Kopřiva, Jan (referee) ; Kunovský, Jiří (advisor)
This thesis discusses the analytical errors emerging from semi-analytical calculations. It also discusses about the modern method of Taylor's series for numerical calculations of ordinary differential equations and chosen methods of charachterized functions. The end solutions indicate favourable results for the semi-analytical calculations in the selected roles and responsible differential equations by direct execution of Taylor's series for solutions of polynomial functions, exponential functions & geometric functions using simulation program "TKSL". It also discusses about the definite & indefinite Intergals and methods for the solution of definite integrals. Followed by a brief introduction of Maple, Matlab & TKSL and further comparison of the result of the three programs & finding the best way of resolving the definite integrals.
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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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Specialized Parallel System and Elementar Processors
Nevřala, Pavel ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
The present thesis deals with the conceptual design of the elementary processor for computation of fixed point. This study will examine and analyze the cooperation of processors in the calculation of linear systems of differential equations with a focus on Euler's method, Runge-Kutta method and Taylor series. The thesis is divided into two major parts. The first part contains the processor design according to the type of communication processor internal components and the type of communication between processors in the calculation. The second part describes the design and implementation of a specialized multi-variant parallel system and a compararison between them.
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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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SSI Dividing Numerical Integrator
Suntcov, Roman ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
The thesis deals with numerical integration and hardware division operations. The reader is familiar with the numerical solution of differential equations through several different methods, for example Taylor's series. Furthermore, it is discussed the operation of division in the hardware and the method of its implementation in the FPGA. Subsequently, a parallel-parallel and serial-parallel integrator is designed. The practical aim of the thesis is to design and implement a serial-serial dividing integrator and create a simulator for it.
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Division Operation Simulation
Matečný, František ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work deals with numerical integration and division operation. The reader is acquainted with the numerical solution of differential equations using division by the Taylor series. Next is explained the principle of SRT division in hardware and introduction of draft of design series-parallel and parallel division integrator in fixed point arithmetic. The practical aim of this work is implementation parallel division integrator and development of a software simulation of this integrator.
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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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