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: 23.10.2023 - 04.12.2023
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): Nuutti Hyvönen
Contact information for the course (applies in this implementation):
Lecturer: Nuutti Hyvönen (first.second@aalto.fi)
Assistant: Duc Khuat (first.second@aalto.fi)
CEFR level (valid for whole curriculum period):
Language of instruction and studies (applies in this implementation):
Teaching language: English. Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
valid for whole curriculum period:
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 for whole curriculum period:
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 exam at 9.00-12.00 on Monday, December 4.
Workload
valid for whole curriculum period:
contact hours 36h (no compulsory attendance)
self-study ca 100h
DETAILS
Study Material
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 for whole curriculum period:
Prerequisites
valid for whole curriculum period:
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Teaching Language : English
Teaching Period : 2022-2023 No teaching
2023-2024 Autumn IIEnrollment :
Sisu (sisu.aalto.fi)
Details on the schedule
applies in this implementation
The first lecture will be at 12-14 on Monday, October 23 in U6 (U149) and the first exercise session at 10-12 on Thursday, November 2 in Y313. There is no exercise session on October 26.
Each week there are four home exercises that are published on Wednesday and should be returned at the latest at 10.15 on Thursday of the following week, i.e., before the exercise session where the solutions of the exercise problems are considered. For example, the first assignments that should be returned at the latest on Thursday, November 2, will be published on Wednesday, October 25.
- Teacher: Hyvönen Nuutti
- Teacher: Khuat Duc