Numerical Methods for Partial Differential Equations - M1 - 8EC

1) Prerequisites

==> Bachelor course(s) on numerical analysis and differential equations!

==> Experience with the package Matlab (or Python): this will be needed for the computer exercises!

Numerical Analysis prerequisites: roundoff errors, interpolation, numerical differentiation and integration, numerical solution of (systems of) non-linear equations, numerical solution of ordinary differential equations: error, stability, accuracy.

Differential Equations prerequisites: existence and uniqueness of local solutions, phase plane analysis, stability of stationary points, properties of linear differential equations with constant and variable coefficients, series solutions of ordinary differential equations, simple boundary value problems.

 

2) Aim of the course

To provide theoretical insight in, and to develop practical skills for, the numerical solution of evolutionary (time-dependent) partial differential equations (PDEs).

Particular emphasis lies on finite difference and finite volume methods for parabolic and hyperbolic PDEs.

The first part of the course treats general concepts (stability, consistency, convergence, method-of-lines, ODE integration methods), whereas the second part deals with more advanced topics, such as, Hamiltonian PDEs, adaptive grids, fractional-order DEs, non-standard methods, traveling waves, inverse problems and several PDE applications.

 

3 ) Homework and Exam:

The final grade will be based on:

15% for Computerexercise 1 (individual)

15% for Computerexercise 2 (individual)

70% Final Exam (at the end of the course): written exam

The grades for the two computerexercises still count as part of the grade after a possible retake.
The grade for the final exam must be at least 5.0.

 

4) Lecture notes /Literature:

 

Weekly lecture notes and exercises (on the webpage of the course).

A useful book that treats most of the course topics of the first part could be: "Finite Difference Methods for Ordinary and Partial Differential Equations" by Randall J. LeVeque, SIAM 2007. Additional literature on numerical time-dependent PDEs will be provided on the webpage of the course, in February 2025.

 

5) Lecturers:

 

P.A. Zegeling (and guest lecturers)