Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.
LEARNING OUTCOMES
You will familiarize yourself with the basic properties of initial value problems for systems of ordinary differential equations. You will learn the fundamental theory about linear multistep methods (definition, consistency, zero-stability, convergence) and Runge-Kutta methods (definition, order conditions, convergence). You will learn to identify a stiff system and to understand the difference between explicit and implicit numerical schemes. You will understand the signifigance of absolute stability and A-stability, and know how to examine the region of absolute stability for a given numerical method. You will familiarize yourself with simple parabolic and hyperpolic initial/boundary value problems and learn how to discretize them with the help of difference schemes. You will practice implementing the introduced methods numerically.
Credits: 5
Schedule: 26.10.2020 - 07.12.2020
Teacher in charge (valid 01.08.2020-31.07.2022): Nuutti Hyvönen
Teacher in charge (applies in this implementation): Nuutti Hyvönen
Contact information for the course (valid 11.10.2020-21.12.2112):
Lecturer: Nuutti Hyvönen (nuutti.hyvonen@aalto.fi)
Assistant: Pauliina Hirvi (pauliina.hirvi@aalto.fi)
CEFR level (applies in this implementation):
Language of instruction and studies (valid 01.08.2020-31.07.2022):
Teaching language: English
Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
Valid 01.08.2020-31.07.2022:
Basic existence and uniqueness results for systems of ordinary differential equations. Linear multistep methods and Runge-Kutta methods: stability, convergence and numerical implementation. Discretization of simple initial/boundary value problems for parabolic and hyperbolic partial differential equations.
Applies in this implementation:
- Week 1: Introduction and motivation
- Weeks 2-3: Linear multi-step methods
- Week 4: Runge-Kutta methods
- Week 5: Parabolic PDEs
- Week 6: Hyperbolic PDEs
Assessment Methods and Criteria
Valid 01.08.2020-31.07.2022:
Teaching methods: lectures, exercises and exam.
Assessment methods: exercises and an exam.
Applies in this implementation:
Half of the grade is based on the exercises and a half on a final online exam at 9.00-12.00 on Monday, December 7.
Workload
Valid 01.08.2020-31.07.2022:
contact hours 36h (no compulsory attendance)
self-study ca 100h
DETAILS
Study Material
Valid 01.08.2020-31.07.2022:
All essential material is included in the lecture notes that are available at the course's homepage.
Applies in this implementation:
Hand-written lecture notes available in MyCourses cover the contents of the course. Most of the lectures roughly follow:
D. F. Griffiths and D. J. Higham, Numerical Methods for Ordinary Differential Equations, Springer.
Substitutes for Courses
Valid 01.08.2020-31.07.2022:
Mat-1.3652
Prerequisites
Valid 01.08.2020-31.07.2022:
MS-A00XX, MS-A01XX, MS-A02XX. The courses MS-A03XX, MS-C134X, MS-C1350, MS-C1650 may also be useful.
FURTHER INFORMATION
Details on the schedule
Applies in this implementation:
The lectures are published on Mondays and Wednesdays.
There are six rounds of exercise problems: they are published on Monday (starting on October 26) and the corresponding solutions should be returned via MyCourses by 17.00 on Wednesday of the following week (the first solutions are due on November 4).
- Teacher: Hyvönen Nuutti