**GNI** text book, **N** note of the course.

Note1 on preliminary material on Runge-Kutta and Linear multi-step.

### Schedule (under construction)

Week | Date | GNI | Other | Learning outcome | Subject | You are required to read on your own |
---|---|---|---|---|---|---|

33 | 22.08.2013 | All | Information meeting | |||

34 | 27.08, 29.08 | Ch. III p 51 | Note1 ch 1, 2, 3, 4.1 | L1 | Theorem of existence and uniqueness of solutions for ODEs and stability theorem (continuous dependence on initial data), theorem of the convergence of the Euler method and of RK methods. Order conditions for RK-methods. | |

35 | 03.09, 05.09 | Ch II.1.2 p 30. | Note1 Ch 6.1-6.3 | L1, L2 | Multi-step methods. 0-stability order barriers. Collocation methods. Talk by the Onsager Professor, Reinout Quispel on the 5th at 14:15 in R9 (instead of the lecture). | |

36 | 10.09, 12.09 | L1 | Collocation methods. Partitioned Runge-Kutta methods. | |||

37 | 17.09, 19.09 | L4, L5 | The activity planned for this week is work on the project, start by finding the topic. Make a plan for what you'll try to achieve in the project. | |||

38 | 24.09, 26.09 | L4, L5 | Adjoint of a method. Composition methods. Splitting and composition methods. Discussion on work done on the project last week, supervision of the project. Continue working on the project. Meeting with the reference group. | |||

39 | 01.10, 03.10 | L1, L4, L5 | Lagrangian and Hamiltonian mechanics. Symplectic transformations. Theorem: The flow of a Hamiltonian vector field is a symplectic map. | |||

40 | 08.10, 10.10 | L2 | Theorem: Locally Hamiltonian vector field. Theorem: Integrability Lemma. Structure preserving integration of Hamiltonian systems. Symplectic integration. Friday 11th supervision of the project 8-12 am. | |||

41 | 15.10, 17.10 | L2 | Preservation of first integrals. Symplecticity of Runge-Kutta methods and preservation of quadratic invariants. | |||

42 | 22.10, 24.10 | L2 | Variational integrators. Project work. | |||

43 | 29.10, 31.10 | diff forms | L2 | Variational integrators. Manifolds, vector fields on manifolds, differential forms, exterior derivative. Theorem: variational integrators are symplectic. Backward error analysis. Supervision of the project on Thursday 31st afternoon 2-4 pm. | ||

44 | 05.11, 07.11 | Note of the course chapter on LGM | L2 | Lie groups and Lie algebras. Properties of the matrix exponential. Lie group methods and methods for integration on manifolds. | ||

45 | 12.11, 14.11 | Note of the course chapter on PDEs | L3 | Methods based on frame vector field and methods using Lie group actions. Magnus methods. | ||

46 | 19.11, 21.11 | L3 | Presentation. Exercises on Hamiltonian PDEs. | |||

47 | 26.11, 28.11 | L3 |