In this paper the rate of convergence, speed of execution and symplectic properties of the time-integrators Leap-Frog (LF2), fourth order Runge-Kutta(RK4) and Crank-Nicholson (CN2) have been studied. This was done by solving the one-dimensional model for a particle in a box (Dirichlet-conditions). The results show that RK4 is the fastest in achieving higher tolerances, while CN2 is the fastest in achieving lower tolerances. Fourth order corrections of LF (LF4)and CN (CN4) were also studied, though these showed no improvements overLF2 and CN2. All methods were shown to exhibit symplectic behavior.

This thesis deals with the synthesis and optimization of frequency analogue filters with modern active elements usable for higher frequencies. The thesis is divided into three parts, the first part deals with the problematic concerning Leap-Frog combined ARC structure. Due to a difficult design, this method is not described in a detail and used in practice, although it shows e.g. low sensitivity. Firstly, a complete analysis of individual filters was made (for and T endings) and consequently these findings were used during implementation of this method to NAF program. Finally, samples of real filters were realized (for verification of functioning and correct design). Another very interesting topic concerning filters is usage of coupled band-pass for small bandwidth, where it is necessary to solve the problems concerning ratio of building elements values, but also price, quality, size of coils, sensitivity, Q factors, coefficients etc. That is why in practice a coil is very often substituted with other equivalent lossy and lossless blocks which create ARC filters structure. The design and the possibility of usage of lossy grounded elements were described here (such as synthetic inductors, frequency dependent negative resistor). Some parts of the design are individual computer sensitivity analysis, setting of usage and quality comparison of individual lossy grounded blocks. Besides, a program for these elements was created, it is useful for a quick design and depiction of transfer characteristics. The third part deals with the usage of tuning universal filters consisting three or more operational amplifiers, which secures its universality and possibility to create different kinds of transfer characteristic. In practice, Akerberg - Mossberg and Kerwin - Huelsman - Newcomb are the most used types of filters. These were also compared with less common universal filters. In the end, the possibility of digital tuning of universal filter with the help of digital potentiometers for filters of 10th order and frequency around 1 MHz was shown.

Master’s thesis deals with the issue of electronic filtering circuits with arbitrary frequency characteristics. First part of the thesis describes theoretical basis. Second part explores the possibilities of design procedures for filters with arbitrary frequency characteristics. Design procedures are demonstrated on examples accordingly to the presented methods, including their circuit implementation and computer simulation to verify the correctness of theoretical assumptions. Thesis also explores the possibilities of tuning circuit structures and electronic setting for characteristics using controllable active elements.