|
|
|
||
Last update: T_KNM (29.04.2015)
|
|
||
Last update: Scott Congreve, Ph.D. (29.10.2019)
The condition for the credit is an active participation at exercices. The nature of the condition excludes the repetition of this check. |
|
||
Last update: Scott Congreve, Ph.D. (29.10.2019)
Deuflhart P., Bornemann F.: Scientific Computing with Ordinary Differential Equations, Springer Verlag, 2002
Hairer E., Norset S.P., Wanner G.: Solving Ordinary Differential Equations I (Nonstiff Problems), Second Revised Edition, Springer Verlag, 1993
Hairer E., Wanner G.: Solving Ordinary Differential Equations II (Stiff and Differential-Algebraic Problems), Springer Verlag, 1991 |
|
||
Last update: Scott Congreve, Ph.D. (29.10.2019)
The exam is composed from the two parts: written and oral. The written part comes first and its passing is the necessary condition to pass the whole exam. The final mark corresponds to the level of knowledge in both parts of the exam.
The written part contains examples related to those in the course syllabus.
The oral part corresponds to the syllabus and the lectures. |
|
||
Last update: T_KNM (29.04.2015)
1) Basic concepts: Examples of evolution processes, systems of ordinary differential equation, initial problem, trajectory, vector field, phase portrait, stationary solution.
2) One-step methods: Examples of one-step methods. Analysis of convergence of a general one-step method. Adaptive choice of length of the time step. Runge-Kutta methods, Butcher's array.
3) Multi-step methods: Idea of numerical integration (Adams-Bashforth, Adams-Moulton, Nyström, Milne-Simpson), predictor-corrector methods. General linear multi-step methods.
4) Dynamical systems: Asymptotics (orbit, limit set), A-stability, Lyapunov theorem. Discrete dynamical systems.
5) A-stability: A-stability region for Runge-Kutta methods. A-stability region for linear multi-step methods. "Stiff" problems, A-stable methods. |
|
||
Last update: prof. RNDr. Vladimír Janovský, DrSc. (15.05.2018)
Bc in mathematics |