### MS-E1652 - Computational methods for differential equations, 30.10.2017-20.12.2017

Credits: 5

Schedule: 30.10.2017 - 20.12.2017

Teaching Period (valid 01.08.2018-31.07.2020):

I Autumn (2018-2019, 2019-2020)

Learning Outcomes (valid 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.

Content (valid 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.

Assessment Methods and Criteria (valid 01.08.2018-31.07.2020):

Teaching methods: lectures, exercises and exam.

Assessment methods: exercises and an exam.

contact hours 36h (no compulsory attendance)

self-study ca 100h

Study Material (valid 01.08.2018-31.07.2020):

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

Substitutes for Courses (valid 01.08.2018-31.07.2020):

Mat-1.3652.

Course Homepage (valid 01.08.2018-31.07.2020):

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

Prerequisites (valid 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.