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One-Step and Multistep Methods: algorithms, convergence analysis.
Dynamical Systems (continuous and discrete time).
Last update: T_KNM (27.04.2006)
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Dynamical systems: theory and numerical approximation. Last update: T_KNM (17.05.2008)
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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: T_KNM (17.05.2008)
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The course consists of lectures in a lecture hall and exercises in a computer laboratory. Last update: T_KNM (17.05.2008)
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Examination according to the syllabus. Last update: T_KNM (17.05.2008)
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ODE: Mathematical model of evolution (examples: population dynamics, chemical oscilations, etc.)
Revising ODE theory: The Existence and Uniqueness Theorems, geometric interpretation of a solution: vector field, phase flow, phase portrait. Taylor expansion of the flow.
One-Step Metods: elementary examples, convegence analysis, adaptive step-size, Runge-Kutta Methods, Implicit methods (Gauss, Radau, linearly Implicit RK, etc.)
Multistep Metods: The methods based on numerical integration and differentiation, Linear Multistep Methods (discretisation error, D-stability, covergence analysis).
Dynamical systems: A long time evolution (orbit, limit set), steady state, A-stability, linearization, Lyapunov Theorem. Discrete time dynamical systems.
A-stability of a method: Domain of A-stability for Runge-Kutta Methods and for linear Multistep Methods. "Stiff" problems. A-stable methods. Last update: T_KNM (17.05.2008)
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There are no special entry requirements. Last update: T_KNM (17.05.2008)
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