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:

Regarding examination

Course Literature

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

Official Course Description

Syllabus in English
Kursplan på svenska

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

Course Evaluations, Numerical Analysis at Faculty of Science