Numerical approximation of finite-difference PDEs

This course introduces some fundamental elements for the numerical approximation of mathematical models of mechanics (partial differential equations). The focus will be on the linear phenomena of diffusion and advection present in all mechanical equations. Most of the course will be devoted to the finite-difference method for one-dimensional problems, studying the essential notions of accuracy, stability, convergence, diffusion and numerical dispersion. Concrete examples will be presented (heat equation, advection of a pollutant in a river, acoustic wave propagation, etc.).

The course outline is as follows:

1. PDEs in mechanics, introduction to numerical simulation
2. Approximation of derivatives by finite differences
3. Numerical approximation of Poisson's equation
4. Numerical approximation of the heat equation
5. Numerical approximation of the advection equation
   
   The numerical methods seen in the course will be the subject of exercises done in TD and will be programmed in Fortran during TP.

- differential and integral calculus - linear algebra - numerical analysis

Applied mathematics, numerical analysis, scientific computing, numerical simulation of physical phenomena