Numerical Methods for Differential Equations

Numerical Methods for Differential Equations

NUMN32 Numerical Methods for Differential Equations, 7.5 credits, is a compulsory course for a Master of Science degree in mathematics. The course can be taken as a stand-alone course. The course is given at half-study pace during the second half of each autumn semester. The course is given in English.

Course Content
The course treats

  • Methods for time integration: Euler’s method, the trapezoidal rule.
  • Multistep methods: Adams' methods, backward differentiation formulae.
  • Explicit and implicit Runge-Kutta methods.
  • Error analysis, stability and convergence.
  • Stiff problems and A-stability. Error control and adaptivity.
  • The Poisson equation: finite differences and the finite element method.
  • Elliptic, parabolic and hyperbolic problems.
  • Time dependent partial differential equations: numerical schemes for the diffusion equation.
  • Introduction to difference methods for conservation laws

Teaching
The teaching consists of lectures and computer projects. Participation in the computer projects is mandatory. Independent problem solving using computers is a central part of the course.

Assessment
Examination consists of a written examination at the end of the course, and presentations of the computer projects during the course.

More information regarding the examination and  a selection of past examination papers is available on the following link:

Course Literature

  • Iserles, A: Numerical analysis of differential equations. Cambridge University Press, 2008, ISBN: 978-0521734905.

Official Course Description

Course Evaluation
Link to course evaluations on the department's website: