DN2255 Numerical Solutions of Differential Equations 7.5 credits

Course contents

Numerical treatment of initial value problems, boundary value problems and eigenvalue problems for ordinary and partial differential equations. The emphasis on different parts may vary from year to year. Relevant linear algebra, well-posedness, convergence, stability, error estimates, finite differences, finite elements, finite volumes, method of lines, modern iterative methods, problems with shocks. Computer labs and application oriented projects.

Intended learning outcomes

The course gives the students knowledge of problem classes, basic mathematical and numerical concepts and properties, modern numerical methods, and software for solution of engineering and scientific problems formulated as differential equations.

After successful completion of course requirements the students will be able to

• design, implement and use numerical methods for computer solution of scientific problems involving differential equations;
• follow specialized and application-oriented technical literature in the area;
• understand properties of different classes of differential equations and their impact on solutions and proper numerical methods;
• use commercial software with understanding of fundamental methods, properties, and limitations

Course disposition

No information inserted

Specific prerequisites

Single course students: 90 university credits including 45 university credits in Mathematics or Information Technology. English B, or equivalent.

Recommended prerequisites

Equivalent to DN2221 Applied Numerical Methods, part 1 and DN2222 Applied Numerical Methods, part 2.

Equipment

No information inserted

Literature

To be announced at least 4 weeks before course starts at course home page. Previous year: R. Le Veque: Finite Volume Methods for Hyperbolic Problems.

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

A, B, C, D, E, FX, F

Examination

• LAB1 - Laboratory Task, 3.0 credits, grading scale: P, F
• LAB2 - Project, 1.5 credits, grading scale: A, B, C, D, E, FX, F
• TEN1 - Examination, 3.0 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

In this course all the regulations of the code of honor at the School of Computer science and Communication apply, see: http://www.kth.se/csc/student/hederskodex/1.17237?l=en_UK.

Other requirements for final grade

Examination (TEN1; 3 university credits).
Computer assignments (LAB1; 3 university credits).
Project (LAB2; 1,5 university credits).

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Patrick Henning

Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Offered by

CSC/Numerical Analysis

Main field of study

Mathematics

Education cycle

Second cycle

Add-on studies

No information inserted

Contact

Patrick Henning (pathe@kth.se)

Supplementary information

This course can be counted in the degree even if the student has taken 2D1225/DN225.