KROULÍKOVÁ, T. Runge-Kuttovy metody [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2018.
The thesis deals with Runge-Kutta methods (RK) used to solve differential equations with initial condition. The first part is devoted to explicit RK methods and the second to the implicit ones. The thesis is well organized and contains reasonable number of misprints with respect to the extent of the text. The main contribution may be found in Sections 2.6 and 2.7 where the author proved and numerically verified that the modified RK methods are of order four for autonomous equations only. Moreover, even embedded RK methods with step size selection were implemented in Matlab and verified. Finally, I declare that the objectives were fulfilled and I recommend the thesis for the defence. As final classification I propose grade B/very good.
| Kritérium | Známka | Body | Slovní hodnocení |
|---|---|---|---|
| Splnění požadavků a cílů zadání | A | ||
| Postup a rozsah řešení, adekvátnost použitých metod | B | ||
| Vlastní přínos a originalita | B | ||
| Schopnost interpretovat dosažené výsledky a vyvozovat z nich závěry | B | ||
| Využitelnost výsledků v praxi nebo teorii | C | ||
| Logické uspořádání práce a formální náležitosti | C | ||
| Grafická, stylistická úprava a pravopis | B | ||
| Práce s literaturou včetně citací | B | ||
| Samostatnost studenta při zpracování tématu | A |
The diploma thesis is devoted to numerical methods of the Runge-Kutta type for an initial value problem with a first order differential equation (system of equations). The goal is to provide a comprehensive overview of the available methods and compare their properties from both the theoretical as well as simulation point of view. It can be stated that the goals of the work have been fulfilled (perhaps, the section devoted to stability of the RK methods could be more extensive). The text draws heavily on the monographs [7], [21], [22] and is supported by a lot of other information based on the cited papers. It is worth to mention several papers by Evans et al. (that introduce some modifications to the classical RK methods) claiming that the resulting methods are of order 4. The author of this thesis, however, shows that this is true for an autonomous equation (system). For a non-autonomous equation, we have a second order method only. Hence, a flaw in the mentioned papers is pointed out. It is also commendable that a set of own MATLAB codes for many of the discussed methods has been created and intensively tested. The text is clearly written and well organized. The used English is quite good, however, the articles should not be ignored (also, some unconventional expressions are used at some places, a bad form of the past tense or plural, etc.). I also have noticed several other imperfections (a bad cross-reference, mentioning a notion which is explained far later in the text, misprints, etc.). Otherwise, I have no serious objections against the formal aspects of the work.
| Kritérium | Známka | Body | Slovní hodnocení |
|---|---|---|---|
| Splnění požadavků a cílů zadání | A | ||
| Postup a rozsah řešení, adekvátnost použitých metod | A | ||
| Vlastní přínos a originalita | C | ||
| Schopnost interpretovat dosaž. výsledky a vyvozovat z nich závěry | B | ||
| Využitelnost výsledků v praxi nebo teorii | A | ||
| Logické uspořádání práce a formální náležitosti | B | ||
| Grafická, stylistická úprava a pravopis | B | ||
| Práce s literaturou včetně citací | B |
eVSKP id 108247