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Numerical Methods for Time- Dependent PDEs
| Credits | 8 credit points |
| Instructors | Zegeling, P. (Universiteit Utrecht) |
| P.A.Zegeling@uu.nl | |
| Aim | 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. |
| Description | Description: The following topics will be treated: * Classification of PDEs, basic examples and applications * Introduction to finite differences (FDs) * Basic theory: convergence, consistency and stability * The Lax theorem * 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 * The method-of-lines approach * Non-uniform and adaptive moving grids |
| Organization | Lectures & excercise classes |
| Examination | Homework & programming assigments |
| Literature | Handouts & the book: W. Hundsdorfer & J.G. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion- |
| Prerequisites | Basic knowledge of analysis, numerical analysis and some programming experience. |