Numerical Methods for Differential Equations, 6 credits

Learning outcomes

Knowledge and understanding
After completed studies, the student shall have

• account for and use the most important numerical methods for ordinary and partial differential, and
• determine suitable methods for a given problem.

Competence and Skills
After completed studies, the student shall be able to

• classify differential equations,
• define and use the concepts consistence, stability and convergence,
• use and analyze the most important numerical methods for ordinary differential equations, ordinary boundary value problems, and the simplest partial differential equations,
• for a given problem identify the type and suggest a solution method, and
• use suitable software for simulation and visualization of the solution to differential equations in some relevant applications.

Content

Consistence, stability and convergence of multistep methods. The most important theorems of G. Dahlquist. Difference methods and finite element methods for ordinary differential equations including error analysis. Convergence analysis for method of lines. Finite difference and finite element methods for elliptic equations in two and three dimensions including error analysis. Finite difference methods for hyperbolic problems in two dimensions with convergence analysis. Mathematical modelling using differential equations. Programming in Matlab.

Examinations and grades

Theory, 3 credits (Code: A001)
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Computer Assignments, 3 credits (Code: A002)
Grades used are Fail (U) or Pass (G).

According to the Higher Education Ordinance, Chapter 6, Section 18, a grade is to be awarded on the completion of a course, unless otherwise prescribed by the university. The university may determine which grading system is to be used. The grade must be determined by a teacher specifically nominated by the university (the examiner).

In accordance with university regulations on grading systems for first and second-cycle courses and study programmes (Vice-Chancellor’s decision ORU 2018/00929), one of the following grades is to be used: fail (U), pass (G) or pass with distinction (VG). For courses included in an international master’s programme (60 or 120 credits) or offered to the university’s incoming exchange students, the A to F grading scale is to be used. The vice-chancellor, or a person appointed by them, may decide on exceptions from this provision for a specific course, if there are special grounds for doing so.

The grades used on this course are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Comments on grades

The grade from the course as a whole is given the grade from the examination part A001, provided that the grade for the examination part A002 is passed.

Grading scale A-F according to the vice-rector's decision 2019-11-12 case no: ORU 06367/2019.

Modes of assessment

• Theory (code A001): Written examination
• Computer Assignments (code A002): Written assignment and oral examination

The re-examination falls within eleven weeks after the regular examination.

For students with a documented disability, the university may approve applications for adapted or other modes of assessment.

For further information, see the university's local examination regulations.

Specific entry requirements

Linear Analysis, 7.5 credits and Computational Mathematics I, 6 credits.

For further information, see the university's admission regulations.

Other provisions

All or part of the course may be given in English.

Students who have been admitted to and registered on a course have the right to receive tuition and/or supervision for the duration of the time period specified for the particular course to which they were accepted (see, the university's admission regulations (in Swedish)). After that, the right to receive tuition and/or supervision expires.

Reading list and other learning resources

Required Reading

Sauer, Timothy (latest edition)
Numerical Analysis
Pearson

Materials provided by the Mathematics Unit.