To provide theoretical insight in, and to develop some practical skills for, numerical solution methods for evolutionary (time-dependent) partial differential equations (PDEs). Particular emphasis lies on finite difference and finite volume methods for parabolic and hyperbolic PDEs.

The following topics will be treated:
* Short intro on numerical methods for ordinary differential equations (ODEs)
* Classification of PDEs, basic examples and applications
* Introduction to finite differences (FDs)
* The method-of-lines approach
* Basic theory: convergence, consistency and stability
* The Lax theorem and Von Neumann stability analysis
* Dispersion, dissipation and modified PDEs
* FDs for parabolic equations
* Extension of techniques to two space dimensions
* FDs and finite volume methods for hyperbolic equations
* Numerical treatment of the wave equation
* Fractional order PDEs
* Non-uniform and adaptive moving grids
* Non-standard finite differences

Prerequisites

Basic knowledge of analysis, numerical analysis and some programming experience (Matlab or Fortran or C++ or ...).