# MA8404 - Numerisk integrasjon av tidsavhengige differensialligninger

# MA8404 - Numerical solution of time dependent differential equations

Messages |
---|

Exam. In question 1 you will be asked to give a short overview of one of the main topics considered in the course. The question will be formulated as follows: "Give an overview summary of what you have learned about the subject ….. Discuss… Choose one particular topic within the subject and explain it in larger detail". Question 2 is a Theorem: you should state the requested theorem and give the proof. (See the list of highlighted theorems under Schedule.). Question 1 and 2 are obligatory questions, which you should attempt to answer. Please do not write a very long answer to the first question, keep it down to 2 or 3 handwritten pages (depending on your handwriting). Then you should answer to 4 more questions which you can pick among 6 or 7 possible questions. |

I have made copies of the notes on differential forms and published them on this webpage. I also highlighted the theorems which can be potentially asked at the exam in boldface under Schedule. |

Supervision of the project on Thursday 31st from 2pm to 4pm in 1346 sentralbygg 2. |

The project paper should not exceed 10 pages, this means 10 pages excluding front page, references and any appendices. |

Tomorrow Thursday 24th no lecture. Work on the project. There will be supervision of the project on Thursday afternoon from 2 to 4 pm next week. |

Friday 11th of October from 8:15 to 12:00 supervision of the project work in my office, 1346 sbII. |

I've updated the information about the project. See under "List of projects". |

On the third of October the Fields medal winner Stanislav Smirnov is visiting NTNU and is giving the Onsager lecture at 13:15 in R8. The title of the lecture is The Ising model of a ferromagnet from 1920 to 2020. You are encouraged to participate. |

I would like to warmly recommend to you the following seminar on the 02.10.2013, 8:15 in PFI Building, Auditorium 5th floor, Tom Huges, Austin, USA, Isogeometric phase-field modelling of brittle and ductile fracture. Tom Huges is a honorary doctor at our University. |

Reference group. All students are members of the reference group. We will have three meetings to discuss the material of the course, the book, the lectures and the achievement of the learning outcome so far in the course. The first meeting will be held on the 24th of September at the end of the lecture. |

On the 17.09 and 19.09 you should work on the project (find the topic) and solve some exercises. The exercises are: Exercise 2, I.6, p. 25; Exercise 1, II.6, p. 50; Exercise 5, II.6, p. 50; Exercise 1, III.6, p. 95 of the book Geometric Numerical Integration. |

On Thursday 5th at 14:15 in R9, this year Onsager Professor, Reinout Quispel from La Trobe University, Australia, will give his lecture and receive the Onsager Medal. His lecture, Geometric Numerical Integration of Differential Equations, will be an introduction to the upcoming topics of our course. Our lecture on Thursday 5th will be replaced by this lecture, you are welcome and encouraged to attend. |

The lectures are in room 734 in Sentral Bygg II. On the 3rd of September the room is busy, I therefore booked room 656 instead (14:15-16). |

Topics covered in MA8404: 1. Differential Algebraic Equations 2. Symplectic methods for Hamiltonian systems. 3. Preservation of invariants, energy-preserving methods and symmetric methods. 3. Lie groups methods. 4. Exponential integrators for highly oscillatory problems and for PDEs. 5. Hamiltonian PDEs (multisymplectic PDEs, energy-preserving methods, symplectic methods for PDEs). |

## Lectures

Tuesdays 14:15-16 in room 734 SBII

Thursdays 10:15-12 in room 734 SBII

## Description and learning outcome

Code | Description | |
---|---|---|

Knowledge | L1 | Classical Runge-Kutta and multistep methods. |

L2 | Structure preserving integrators. | |

L3 | Numerical integration methods for PDEs, multi-symplectic integration, highly oscillatory problems. | |

Skills | L4 | Ability to choose and implement a suitable integration method for a given application in a range of applied and theoretical problems (for example problems in mechnics). |

L5 | Ability to choose and implement a suitable integration method given a particular time-dependent PDE. | |

General competence | L6 | Ability to participate in scientific discussions regarding the topics of the course. |

L7 | Ability to formulate and attack related simple research problems. |

## Lecturer

- Elena Celledoni rom 1346

## Participants

- Markus Eslitzbichler
- Lu Li
- Fabio De Marco
- Christina Frost
- Lars Vingli Odsæter
- Filippo Remonato
- Åsmund Ervik
- Oyvin Bergland Leknes
- Chai Wei

### Reference group

Given there are nine participants to this course, everyone of these is a member of the reference group.

## Book

**Geometric Numerical Integration**

Hairer, Lubich and Wanner, Springer

Other sources:

- Solving Ordinary differential equations vol 1 and 2, Harier, Nørsett and Wanner and Hairer and Wanner.
- notes of MA8404 (These notes will be updated during the semester).

## Project

The participants to this course will choose a topic relevant to their own PhD/master studies and use methods and /or techniques learned in this course to solve (simulate, explain) the problem.

Example 1: given that you are interested in approximating some sort of Hamiltonian systems in your PhD work, one could consider a range a symplectic methods and compare their performance. The main focus in the project could be to illustrate qualitative properties of the problem which one considers and of the methods used.

Example 2: suppose you have learned a certain proof or a technique to perform stability anaylsis which can be applied in a problem which is considered in your PhD work perhaps in a simplified version, you can try to perform a preliminary analysis of the same type in your context.

The learning goal of the project is to try to use to the extent possible what you learn in the course in your own reserach.

There will be a presentation of the project work both in written and oral form. The project will contribute to 30% of the final mark.

Maximum number of pages per project: **10**

See also under "List of projects".

Project presentation: **November 19th.**