Prerequisites
Bachelor courses on numerical analysis and differential equations.
Experience with the package Matlab or Python (or a similar language, for example, Fortran, C++, ...): ===> 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.
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.
Lecturers
P.A. Zegeling (and guest lecturers)
- Docent: Paul Zegeling