MS-E1652 - Computational Methods for Differential Equations D, Exam, 13.12.2021-13.12.2021

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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: 13.12.2021 - 13.12.2021

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):

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.

     

DETAILS

Study Material

  • valid for whole curriculum period:

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

     

Substitutes for Courses
Prerequisites

FURTHER INFORMATION

Further Information

  • valid for whole curriculum period:

    Teaching Period:

    2020-2021 Autumn II

    2021-2022 Autumn II

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

    Registration for Courses: In the academic year 2021-2022, registration for courses will take place on Sisu (sisu.aalto.fi) instead of WebOodi.

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