### MS-E1652 - Computational methods for differential equations, 09.09.2019-23.10.2019

Omfattning: 5

Tidtabel: 09.09.2019 - 23.10.2019

Undervisningsperiod (är i kraft 01.08.2018-31.07.2020):

I Autumn (2018-2019, 2019-2020)

Lärandemål (är i kraft 01.08.2018-31.07.2020):

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.

Innehåll (är i kraft 01.08.2018-31.07.2020):

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.

Metoder, arbetssätt och bedömningsgrunder (är i kraft 01.08.2018-31.07.2020):

Teaching methods: lectures, exercises and exam.

Assessment methods: exercises and an exam.

Arbetsmängd (är i kraft 01.08.2018-31.07.2020):

contact hours 36h (no compulsory attendance)

self-study ca 100h

Studiematerial (är i kraft 01.08.2018-31.07.2020):

All essential material is included in the lecture notes that are available at the course's homepage.

Ersättande prestationer (är i kraft 01.08.2018-31.07.2020):

Mat-1.3652.

Kursens webbplats (är i kraft 01.08.2018-31.07.2020):

https://mycourses.aalto.fi/course/search.php?search=MS-E1652

Förkunskaper (är i kraft 01.08.2018-31.07.2020):

MS-A00XX, MS-A01XX, MS-A02XX. The courses MS-A03XX, MS-C134X, MS-C1350, MS-C1650, MS-E1651 may also be useful.

Bedömningsskala (är i kraft 01.08.2018-31.07.2020):

0-5