The overall goal of the course is to give you knowledge and tools to formulate, analyze and implement numerical algorithms for solving mathematical models from scientific and engineering applications.

The course covers ordinary differential equations and partial differential equations.

Course structure/Navigation

Lectures
On this page you find the lecture schedule, recommended reading and exercises for each lecture, as well as lecture slides and notes.
Most lectures are in period 1 and a few in period 2.
Computer exercises
There are 3 computer exercises in which you work (alone or in pairs) on a set of problems that are solved with numerical methods using Matlab. The exercises involve both implementations and some analysis. Deadline for the first two computer exercises are in period 1 and the deadline for the third computer exercise is in period 2.
Project
There is one larger project towards the end of the course. There are several projects available within different application areas and they are done in groups of up to four students. Project presentations are held on December 8 and 10.

Teachers

Anna Nissen (anissen@kth.se): Lectures, examiner
Roman Stuhlmacher (romanst@kth.se) Lab assistant, exercise lectures

Course literature

Randall. J LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, Society for Industrial and Applied Mathemathics 2007.
The book is available as an eBook at the KTH library. See also the book homepage for exercises and Matlab-files.

Some description of Matlab, e.g. C. Edlund, Matlab i korthet, or the Dundee MATLAB report. There are many Matlab tutorials available on the internet, among them Mathwork's own self study courses, for instance the introductory Matlab Onramp.
Excerpts from A first course in numerical analysis of differential equations by A. Iserles:
- Multistep methods
  Focus on the ideas rather than the proofs.

Examination

There are three parts of the examination. Each must be passed to finish the course:

Computer exercises (max score 30)
Required: At least 18 points in total and at least half the max points on each exercise.
Project (pass/fail)
Required: Oral presentation and Matlab code, pass.
Exam (max score 30)
Required: At least 14 points.

The final grade is determined by the sum of the scores from the computer exercises and the exam (max 30+30 = 60 points) according to the following table:

E	D	C	B	A
32-36.75	37-41.75	42-46.75	47-51.75	52-60

Note that no use of generative AI tools are allowed in the course's graded assignments and exams, see more here.

Exam

The exam is a five hour exam on 2026-01-12, at 8-13. Do not forget to sign up for the exam. To sign up you need to be registered for the term as well as the course. If for some reason you cannot sign up, please contact the student office at studentoffice@math.kth.se

The material included in the exam is:

Chapters 1-3, 5-10 in the course book: Randall. J LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, Society for Industrial and Applied Mathemathics 2007.
Lecture slides.
Material on multistep methods (excerpts from A first course in numerical analysis of differential equations, see above.)
Material in Computer Exercises 1-3.

Examples of earlier exams from the previous courses (in particular SF2520) and the two given exams for SF2527 are found below. On the Lecture page there are lists of which exam questions that are relevant for each part of the course.

Exams for SF2527:

Students with disabilities may have the right to certain compensatory support for example during examination.