*The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.*

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1 |
1.4 , 1.7, 2.1, 2.3, 2.4 3.3 4.1 5.1 6.1, 6.4
At the end of this teaching unit, the student will be able to:
1. explain the importance and interest of numerical simulation methods in physics; 2. analyse the stability, convergence and accuracy of a numerical method; 3. compare alternative numerical methods for solving a differential equation; 4. design a methodology for solving a given physical problem by numerical simulation; 5. write a report on solving a physical problem by numerical simulation. |

*The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.*

2. Finte difference methods

a. Initial condition problem (ordinary differential equations)

b. Boundary condition problem

c. Diffusion

d. Advection

e. Waves

3. Spectral methods for the resolution of

a. ordinary differential equations

b. partial differential equations

- Exercises framed as small projects in computer room.

- L. N. Trefethen, Spectral methods in Matlab, SIAM publications, Oxford, 2000.

- D. Gottlieb et S. A. Orszag, Numerical analysis of spectral methods: Theory and applications, SIAM, 1986.

**PHYS**