### MS-E1652 - Computational Methods for Differential Equations D, 26.10.2020-07.12.2020

Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), 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 (applies in this implementation):

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
• 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.

##### Assessment Methods and Criteria
• Valid 01.08.2020-31.07.2022:

Teaching methods: lectures, exercises and exam.

Assessment methods: exercises and an exam.

• 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.

##### 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.