Numerical Methods for Differential Equations
Official Course Description
The overarching goal of the course is that the students on completion of the course should know the basics of numerical analysis for differential equations. This includes the construction, analysis, implementation and application of numerical methods for initial value problems, boundary value problems and different types of partial differential equations. 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.
Admission to the course requires English 6 and at least 90 credits in mathematics and/or numerical analysis including the course NUMN19 Numerical Approximation, 7.5 credits, or corresponding.