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Numerical Methods for Ordinary Differential Equations (3V, 1Ü)
Dr. Max WinklerSS2018
Contents
Ordinary differential equations frequently arise when modelling physical processes and the computation of these kind of problems is sometimes very hard, or even impossible. To this end, the constuction and investigation of numerical methods for the computation of these kind of problems is of interest. An important part of this lecture is also the implementation of the numerical methods in Matlab.Goals of this class
Goals of this class are:
- the construction of adapted numerical methods for the solution of ordinary differential equations.
- the implementation of these methods in Matlab
- the convergence and stability analysis of these methods
- the application to complex real-world problems
Dates
| 3 Veranstaltungen aus dem Archiv des Vorlesungsverzeichnisses (Wintersemester 2018/19) | |||||
|---|---|---|---|---|---|
| Nummer | Name | Gruppen | Dozenten | Zeit | Raum |
|
220000-A90
[WS2018/19]
|
Numerical Methods for ODEs
[Vorlesung]
|
obl: M_MROp3 wo: B_MaIn5, M_MaFM1, M_MaMa1, M_MaTM1, MPIM__*, M_MaFM3, M_MaMa3, M_MaTM3, B_MaMa5, B_MaTM5, B_FM__5, B_MT__5, B_WM__5 fak: M_MaIn1, M_MaWM1, M_MaWM3, M_MaIn3 |
Dr. Max Winkler (225033) |
Freitag (wö.) 07:30-09:00 |
2/N002 |
|
220000-A90A
[WS2018/19]
|
Numerical Methods for ODEs
[Vorlesung]
|
obl: M_MROp3 wo: B_MaIn5, M_MaFM1, M_MaMa1, M_MaTM1, MPIM__*, M_MaFM3, M_MaMa3, M_MaTM3, B_MaMa5, B_MaTM5, B_FM__5, B_MT__5, B_WM__5 fak: M_MaIn1, M_MaWM1, M_MaWM3, M_MaIn3 |
Dr. Max Winkler (225033) |
Dienstag (1. Wo.) 11:30-13:00 |
2/N002 |
|
220000-A91
[WS2018/19]
|
Numerical Methods for ODEs
[Übung]
|
obl: M_MROp3 wo: B_MaIn5, M_MaFM1, M_MaMa1, M_MaTM1, MPIM__*, M_MaFM3, M_MaMa3, M_MaTM3, B_MaMa5, B_MaTM5, B_FM__5, B_MT__5, B_WM__5 fak: M_MaIn1, M_MaWM1, M_MaWM3, M_MaIn3 |
Dr. Max Winkler (225033) |
Dienstag (2. Wo.) 11:30-13:00 |
2/N002 |
News
| 26.07.2018 | The lecture and the exercise class start in the first week of the semester. First lecture: Tuesday, 09.10.2018 |
|---|---|
| 25.01.2018 | The lecture at 25th January 2019 will be canceled. |
Additional lecture material
- Numerical methods
- Euler explicit
- Euler implicit with fixed-point iteration
- Euler implicit with Newton's method
- Runge-Kutta-Fehlberg 4(5) (template only), requires ButcherDiagram45
- Helpful functions
- plot_stability_region.m (Plot stability region for a given stability function)
- stabfun_butcher.m (Generate stability function for an RKM with given Butcher table
- eval_root_locus_curve.m (Generate root locus curve for the stability region of an MSM)
- compute_coeffs_AB.m, compute_coeffs_AM.m, compute_coeffs_BDF.m (Helpfull scripts to calculate the coefficients of Adams-Bashforth-, Adams-Moulton- and BDF-methods)
- Test scripts
- simple_pendulum.m (Demonstration of a simple pendulum)
- predator_prey.m (Solution of a Predator-prey model)
- convergence_test.m (for Homework 1)
- dahlquist_test.m (to check A-stability)
- rkm_stability_region.m (draw stability regions for several explicit and implicit RKM
- theta_method_stability.m (draw stability region for the theta-method for different values of theta)
- demo_stiff_n4.m (demonstration of instability effects for a stiff ODE system)
- Van_der_Pol.m (adaptive solution of the van-der-pol oscillator using the Matlab routine ode23s)
- erkm_test.m (tests and compares several explicit RKM, needed for Homework 5)
- satellite.m (solves the satellite problem with an embedded RKM, for Homework 8)
- rkm_stability_region.m, plot_stability_region_msv2.m (draw stability regions for several multistep methods)
- Handouts
Tutorials
| Exercise | Additional material |
|---|---|
| 1. Exercise Sheet | |
| 2. Exercise Sheet | |
| 3. Exercise Sheet | |
| 4. Exercise Sheet | |
| 5. Exercise Sheet | |
| 6. Exercise Sheet | |
| 7. Exercise Sheet |
Exam
There will be an oral examination for participants after the end of the class.Supplementary References
Bücher und Vorlesungsskripte- R. Rannacher: Vorlesungsskript Numerik 1
- M. Herrmann: Numerik gewöhnlicher Differentialgleichungen. Band 01 (zur Ausleihe in der Bibliothek verfügbar)
- K. Strehmel, R. Weiner, H. Podhaisky: Numerik gewöhnlicher Differentialgleichungen (als E-Book über die Bibliothek verfügbar)