Numerical solution of differential equations: Finite difference methods (NumDiff)

Course content

 

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The knowledge topics in the learning outcome are introduced and work is done on building the expected skills and competences.

Education

PhD programme in Natural Science and IT

Learning outcome

Knowledge about
the theory of and computer solution tools for certain standard but also examples of more advanced (based on highest level of international research) difference methods for the numerical solution of the following basic types of ordinary and partial differential equations:
1. Initial value problems for ODE’s.
2. Boundary value problems for ODE’s
3. Diffusion problems for 2nd order PDE’s
4. Advection problems for 1st order PDE’s
5. Wave problems for 2nd order PDE’s
6. Elliptic problems for 2nd order PDE’s.
Skills to
1. apply the methods and tools within the course subject.
2. access theoretical and practical problems and select appropriate solution methods based on theoretical knowledge.
3. inform about problems and solution methods to equals and non-specialists or collaborators and end users.
Competences to independently and professionally
1. participate in individual and interdisciplinary collaboration within the course subject.
2. extend own competences within the course subject.

In week 1-6: 7 hour lectures [l] and 5 hour (math and computer) consulting [c]. 6 l + 6 c in week 7.

MatIntro, LinAlg, and experience with numerical analysis and programming for example obtained in SciComp, NumIntro, NumSDL or POP

To get on the spot help during the exercises, it is assumed that each participant will bring a notebook computer to the exercises. If power is required, an extension cord with at least two connections must be brought.

The course is additionally intended for the bachelorstudies in Actuarial Mathematics, Mathematics-Economics, Mathematics, Computer Science, Physics, Chemistry and other BSc, MSc and PhD programmes with the relevant prerequicites.

Further information about NumDiff is contained in the following "click-and-print" PDF-document: NumDiff.pdf accessible from http:/​/​www.math.ku.dk/​~hugger/​

ECTS
7,5 ECTS
Type of assessment
Written assignment, 2 weeks (half time)
Aid
All aids allowed
Marking scale
passed/not passed
Censorship form
No external censorship
Several internal examiners
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
With reference to terms and numbering in the field "Learning Outcome" the following criteria for assessment are applied:
Knowledge:
Knowledge points are assessed only when they are relevant for the exam project. When relevant a knowledge point is valued according to the extent of knowledge presented.
Skills:
Skill points 1 and 2 are valued according to the extent of skills presented.
Skill point 3 is assessed through the exam registration requirements and not through the exam.
Competencies:
Competency point 1 is assessed through the exam registration requirements and not through the exam.
Competency 2 is valued based on the extent to which the knowledge from different subjects has been combined and extended in the application to the exam project.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 50
  • Theory exercises
  • 34
  • Preparation
  • 76
  • Exam
  • 46
  • English
  • 206