course-details-portlet

TMA4212

Numerical Solution of Differential Equations by Difference Methods

Credits 7.5
Level Third-year courses, level III
Course start Spring 2026
Duration 1 semester
Language of instruction English
Location Trondheim
Examination arrangement Aggregate score

About

About the course

Course content

Difference schemes for different types of partial differential equations. Analysis of consistency, order, stability and convergence. Solution of linear systems by iterative methods and preconditioning. Finite element method.

Learning outcome

1. Knowledge. The student understands the basic theory underlying the numerical solution of partial differential equations. The student masters error analysis of difference methods, and understands the concepts consistency, stability and convergence. The student has a basic understanding of the finite element method and iterative solution techniques for systems of equations.

2. Skills. The student is able to choose suitable methods for elliptic, parabolic and hyperbolic partial differential equations. The student is able to set up, implement and analyze discretization methods for selected partial differential equations. The student is able to design numerical experiments serving the purpose to verify if a PDE-solver is implemented correctly. The student is able to choose and apply suitable iterative methods for equation solving.

3. General competence. The student masters written and oral presentation of scientific problems and of the results obtained in the project work. The student is able to apply aquired mathematical knowledge in linear algebra and calculus to achieve the other goals of the course.

Learning methods and activities

Lectures, project and exercises.

Further on evaluation

In order to pass the course, a passing grade (A-E) in the written exam is required.

The portfolio consists of one project work. A more detailed descripttion of the form of the project presentation will be published on the webpage of the course at the start of the semester.

The re-sit examination for the written exam may be given as an oral examination. The re-sit exam is in August. There will be no re-sit examination for the portfolio. Students are free to choose Norwegian or English for written assessments or the portfolio.

Course materials

Will be announced at the start of the course.

Subject areas

  • Mathematics
  • Technological subjects

Contact information

Course coordinator

Lecturers

Department with academic responsibility

Department of Mathematical Sciences

Examination

Examination

Examination arrangement: Aggregate score
Grade: Letter grades

Ordinary examination - Spring 2026

School exam
Weighting 70/100 Examination aids Code C Duration 4 hours Exam system Inspera Assessment Place and room Not specified yet.
Portfolio
Weighting 30/100

Re-sit examination - Summer 2026

School exam
Weighting 70/100 Examination aids Code C Duration 4 hours Exam system Inspera Assessment Place and room Not specified yet.