Numerics of Differential Equations (Module: MA 3301)
Organisatorial
Lecture | Prof. Dr. B. Wohlmuth Tue. 10:15-11:45 in MI HS 3 Fr. 8:30-10:00 in MI HS 3 |
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Office hours | Prof. Dr. Barbara Wohlmuth, Tuesday 12:15 - 13:15 in MI 03.10.057 Tutors, by arrangement (email) |
Exercises | Tobias Köppl Group 1: Tuesday, 12:15 - 13:45 in MI 02.08.011; Tutor: Christian Waluga (German) Group 2: Wednesday, 10:15 - 11:45 in MI 03.10.011; Tutor: Stefan Karpinski (German) Group 3: Wednesday, 14:15 - 15:45 in MI 03.08.011; Tutor: Stefan Karpinski (German) Group 5: Tuesday, 15:00 - 16:30 in MI 02.10.011; Tutor: Christian Waluga (German) |
Tutorial "Implementation of PDEs" | Dr. C. Waluga, S. Karpinski In some weeks, additional training in the "Kleine Rechnerhalle" (Thursday, 16:00 - 19:00) will be offered. Dates will be announced in the lectures, exercises, and on this webpage. |
General information
- The post-exam review (Klausureinsicht) will take place on Friday, March 15, 15:00-16:30 in 03.010.37
- The final exam will take place on Friday, March 1, 14:00-15:30 in "MI, Hörsaal 1"
- The fourth and last programming tutorial will take place Thursday, January 24, 4-7pm in "Kleine Rechnerhalle".
- The third programming tutorial will take place Thursday, December 13, 4-7pm in "Kleine Rechnerhalle".
- No lecture on Tuesday, November 13, due to the Student plenary meeting. Please return your exercise sheets on Friday. Due to the resulting delay, the upcoming programming tutorial is also postponed to Thursday, November 22, 4-7pm in "Kleine Rechnerhalle".
- Tutor group 4 was replaced by group 5, as asked for by the students
- The first programming tutorial will take place Thursday, October 25, 4-7pm in "Kleine Rechnerhalle".
- The first tutor groups will be held on Tuesday, October 23 and Wednesday, October 24, respectively.
- Please notice that dates and room numbers are subject to change.
- Please register for one of the exercise groups via TUM-Online until Friday, October 19, 2012.
Slides and Exercise sheets
- Exercise sheets
- Sheet 1 (with C,D added to Brusselator)
- Aufgabe4b.m
- Tutorial sheet 1, Getting started
- Sheet 2
- Sheet 3
- m_files_sheet_3.zip
- Sheet 4
- Sheet 5
- m_files_sheet_5.zip
- Tutorial sheet 2, Code Template
- Sheet 6 (Update: 2 indices corrected in Ex. 21 and Ex. 23,added squares in Ex. 22) , bloodflow.m, leapfrog.m, newmark.m
- Sheet 7, ErrorNewmark.zip, Slopelimiter.zip
- Sheet 8
- Tutorial sheet 3, Code Template
- Sheet 9, Aufgabe34.zip
- Sheet 10
- Sheet 11
- Sheet 12
- Sheet 13 (Update: vector \xi updated in exercise 51)
- m_files_sheet_13.zip
- Tutorial sheet 4, Code Template
- Sheet 14
- Solutions
- Solution Sheet 1
- Tutorial solutions 1: ex 1, ex 2, ex 3
- Solution Sheet 2
- sol_m_files_sheet_3.zip
- Solution Sheet 3
- Exercise13c.m
- Solution Sheet 4
- Solution Sheet 5
- sol_m_files_sheet_5.zip
- Tutorial solutions 2: ex 4
- Solution Sheet 6
- sol_m_files_sheet_6.zip
- Solution Sheet 7, ErrorNewmark_lsg.zip, Slopelimiter_lsg.zip
- Solution Sheet 8
- Tutorial solutions 3: ex 6, ex 7.1, ex 7.2
- Solution Sheet 9, Aufgabe34_lsg.zip
- No homework on Sheet 10
- Solution Sheet 11
- Solution Sheet 12
- Solution Sheet 13
- sol_m_files_sheet_13.zip
- Tutorial solutions 4: heatequation
- No homework on Sheet 14
- Slides
- Introduction
- Chapter I: Stiff ODEs (last updated on October 30)
- Chapter II: Classification of PDEs (last updated on October 30)
- Chapter III: Transport Equations in 1D (last updated on November 13)
- Chapter IV.1: Finite Difference Methods (last updated on December 4)
- Chapter IV.2: Finite Element Methods in 1D (last updated on December 7)
- Chapter IV.4: Finite Element Methods in 2D (last updated on January 7)
- Chapter IV.5: Finite Element Methods in 2D (last updated on February 5)
- Chapter V: Parabolic Equations (last updated on February 5)
- Further material
Content
- Modul MA 3301 of the bachelor program in mathematics
Exam
- A written exam will take place at the end of the term. The exam can be repeated before the next summer term.
- A mark of at least 4.0 is required to pass the exam.
- Dates and location of the exams will be communicated via TUM-Online and the web page.
- Apart from 4 pages (2 sheets) handwritten notes, no further auxiliary material is allowed.
- A bonus for the exam can be obtained from the exercises (see next section)
Bonus system
- 80% of homework credits is required to obtain an extra bonus for the final exam
- Homework credits are awarded if the tutors conclude that
- 1) the students put serious effort in the solution of the exercise
- 2) the solution catches the main mathematical ideas of the exercise
- The bonus improves the final mark by one step, f.e. from 2.3 to 2.0
- The mark 1.0 can not be further improved
- The bonus is only applied, if the exam is passed without!!! That is, it does not improve the marks 4.3, 4.7 or 5.0
- Students should keep their homeworks to prove their eligibility for the exam bonus
- One student can submit his or her homework together with up to two other students
Literature
Ordinary differential equations:- Deuflhard, Bornemann: Numerische Mathematik II, 2. Auflage, deGruyter 2002.
- Hairer, Lubich, Wanner: Geometric Numerical Integration, 2nd ed. , Springer, 2006.
- Hairer, Nørsett, Wanner: Solving Ordinary Differential Equations I - Nonstiff Problems, Springer Verlag, 1993.
- Hairer, Wanner: Solving Ordinary Differential Equations II - Stiff and Differential-Algebraic Problems, Springer Verlag, 2002.
- Stoer, Bulirsch: Numerische Mathematik 2, Springer, 2005.
- Grigorieff: Numerik gewöhnlicher Differentialgleichungen 1, Teubner, 1973.
- Grigorieff: Numerik gewöhnlicher Differentialgleichungen 2, Teubner, 1977.
- Strehmel, Weiner: Numerik gewöhnlicher Differentialgleichungen, Teubner, 1995.
- Butcher: The numerical analysis of ordinary differential equations, Wiley, 1987.
- Ascher, Petzold: Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, 1998.
- D. Braess: Finite Elemente. Theorie, schnelle Loeser und Anwendungen in der Elastizitaetstheorie., Springer-Lehrbuch, 2003.
- W. Hackbusch: Elliptic differential equations: theory and numerical treatment., Springer Series in Computational Mathematics 18, Springer-Verlag, 1992.
- A. Quarteroni, A. Valli: Numerical approximation of partial differential equations., Springer Series in Computational Mathematics 23, Springer-Verlag, 1994.
- C. Großmann, H.G. Roos: Numerische Behandlung partieller Differentialgleichungen, 3. Auflage, Teubner-Verlag, 2005
- P. Knabner, L. Angermann: Numerik partieller Differentialgleichungen. Eine anwendungsorientierte Einführung, Springer-Verlag, 2000.
- K.W. Morton, D.F. Mayers: Numerical solution of partial differential equations. An introduction., Cambridge University Press, 2005.
- K. Eriksson, D. Estep, P. Hansbo, C. Johnson: Computational differential equations., Cambridge University Press, 1996.
- H. P. Langtangen. Python Scripting for Computational Science, Springer, 2012.
- P. Solin et al.: Introduction to Python Programming, FEMhub Inc., 2012. (download) ^{}
- Logg, Mardal, Wells. Automated Solution of Differential Equations by the Finite Element Method ^{}. Springer, 2012. (download) ^{}
Links
- Python Programming Language ^{}
- SciPy: Scientific Python ^{}, see also NumPy for Matlab Users ^{}
- FEniCS Project ^{}