Numerical Solution of Differential Equations

Postgraduate course

Course description

Objectives and Content


The course deals with the numerical solution of differential equations and systems of non-linear equations.


Multistep methods as well as Runge-Kutta method for timedependent problem will be examined. Covergence, order and stability properties will be analysed. For boundary value problems we will have a look at finite difference, finite element and spectral methods.

For solving system of non-linear equations we will study fixpoint iteration and Newton's method, and discusse their convergence properties.

Learning Outcomes

On completion of the course the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:


The student

  • has knowledge of state-of-the-art numerical methods in the field.
  • Knows the convergence conditions for the different methods.
  • Knows which order the different methods have and what exactly the term order means.
  • Understands the concept of stiff differential equations, A-stability and stability domain for the different numerical schemes.
  • Knows different spatial discretization schemes, such as: finite differences, finite elements and spectral methods.


The student

  • is able to used the methods in numerical calculations. That is; to be able to implement them on a computer.
  • is able to analyse the order of a numerical method.
  • Understands the possibilities and the limitations of the different methods.

General competence

The student

  • is able to make intelligent choices of method for specific problems
  • converses easily and unforced about topics such as pros and cons in explicit vs implicit methods

Semester of Instruction

Required Previous Knowledge
Recommended Previous Knowledge
MAT160 Scientific computing I
Credit Reduction due to Course Overlap
INF260: 10 ECTS
Compulsory Assignments and Attendance
Forms of Assessment
Written examination 4 hours
Grading Scale
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.
Examination Support Material
Non- programmable calculator, according to model listed in faculty regulations.